MSM2_all.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MSM UTIL"
   ]
  },
  {
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pandas import DataFrame as df\n",
    "from numpy import matlib\n",
    "from scipy.optimize import fminbound, minimize, fsolve\n",
    "from lmfit import minimize, Minimizer, Parameters, Parameter, report_fit\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets, linear_model\n",
    "from sklearn.metrics import mean_squared_error, r2_score\n",
    "from datetime import date\n",
    "#import winsound\n",
    "from pylab import rcParams"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## T_mat_temp"
   ]
  },
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   "source": [
    "def T_mat_temp(kbar):\n",
    "    \"\"\"\n",
    "    Build template for kbar\n",
    "    :param kbar:\n",
    "    :return:\n",
    "    \"\"\"\n",
    "    A = np.fromfunction(lambda i, j: i ^ j, (2**kbar, 2**kbar), dtype=int)\n",
    "    A_temp = A.astype(float)\n",
    "    return A_temp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MSM_starting_values(data, startingvals, kbar):"
   ]
  },
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   "execution_count": 3,
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   "source": [
    "def MSM_starting_values(data, startingvals, kbar):\n",
    "    \"\"\"\n",
    "    find starting values for params\n",
    "    :param data:\n",
    "    :param startingvals:\n",
    "    :param kbar:\n",
    "    :return:\n",
    "    \"\"\"\n",
    "\n",
    "    # print('No starting values entered: Using grid-search')\n",
    "    # A grid search used to find the best set of starting values in the\n",
    "    # event none are supplied by the user\n",
    "    \n",
    "    if bool(startingvals):\n",
    "        dum = startingvals[1]\n",
    "        b = [1.5, 1.5 + (dum-1.5)/3, 1.5 + 2*(dum-1.5)/3, dum]\n",
    "        lb = len(b)\n",
    "        \n",
    "        dum = startingvals[2]\n",
    "        g = [dum, (0.99-dum)/2+dum, .99]\n",
    "        lg = len(g)\n",
    "        sigma = startingvals[3]\n",
    "        \n",
    "    else :\n",
    "        b = [1.5, 3, 6, 20]\n",
    "        lb = len(b)\n",
    "        g = [.1, .5, .99]\n",
    "        lg = len(g)\n",
    "        sigma = np.std(data, ddof=1) #* np.sqrt(252)\n",
    "            \n",
    "        \n",
    "    \n",
    "\n",
    "    LL_storage = df(columns=['LL', 'b', 'g', 'm','sigma'])\n",
    "    m0_lower = 1.2\n",
    "    m0_upper = 1.8\n",
    "\n",
    "    index = 1\n",
    "\n",
    "    # I know that adding one by one row on DF is quiet inefficient\n",
    "    # I will try to use lambda, map instead of double for loop if I have a time\n",
    "\n",
    "    for i in range(0, lb):\n",
    "        for j in range(0, lg):\n",
    "            a_m0 = fminbound(MSM_likelihood_new, 1.2, 1.8,\n",
    "                             args=(b[i], g[j], sigma, kbar, data),\n",
    "                             xtol=1e-05, maxfun=500, full_output=True)  # , disp=3)\n",
    "            LL_storage.loc[len(LL_storage), 'LL'] = a_m0[1]\n",
    "            LL_storage.loc[len(LL_storage) - 1, 'b'] = b[i]\n",
    "            LL_storage.loc[len(LL_storage) - 1, 'g'] = g[j]\n",
    "            LL_storage.loc[len(LL_storage) - 1, 'm'] = a_m0[0]\n",
    "\n",
    "    LL_storage = LL_storage.sort_values(by=['LL'], ascending=True)\n",
    "    LL_storage = LL_storage.reset_index(drop=True)\n",
    "    print(LL_storage)\n",
    "    startingvals = [0., 0., 0., sigma]\n",
    "    startingvals[1] = LL_storage.loc[0, 'b']\n",
    "    startingvals[0] = LL_storage.loc[0, 'm']\n",
    "    startingvals[2] = LL_storage.loc[0, 'g']\n",
    "\n",
    "    return startingvals, LL_storage"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
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   },
   "source": [
    "## MSM_likelihood_new(*args):"
   ]
  },
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    "def MSM_likelihood_new(*args):\n",
    "    \"\"\"\n",
    "    calculate LL for 3 cases (depend on number of input)\n",
    "    :param args:\n",
    "    :return:\n",
    "    \"\"\"\n",
    "\n",
    "    if len(args) ==3 :\n",
    "        # choose starting val\n",
    "        inp = args[0]\n",
    "        kbar = args[1]\n",
    "        data = args[2]\n",
    "        m0 = inp['m0'].value\n",
    "        b = inp['b'].value\n",
    "        gamma_k = inp['gamma_k'].value\n",
    "        sigma = inp['sigma'].value\n",
    "\n",
    "    elif len(args) == 6 :\n",
    "        #\n",
    "        m0 = args[0]\n",
    "        b = args[1]\n",
    "        gamma_k = args[2]\n",
    "        sigma = args[3]\n",
    "        kbar = args[4]\n",
    "        data = args[5]\n",
    "\n",
    "    elif len(args) == 4 :\n",
    "        # prediction\n",
    "        inp = args[0]\n",
    "        kbar = args[1]\n",
    "        data = args[2]\n",
    "        m0 = inp['m0'].value\n",
    "        b = inp['b'].value\n",
    "        gamma_k = inp['gamma_k'].value\n",
    "        sigma = inp['sigma'].value\n",
    "\n",
    "    A_temp = T_mat_temp(kbar)\n",
    "    k2 = 2 ** kbar\n",
    "\n",
    "    def transition_mat(A_temp, b, gamma_k, kbar):\n",
    "        A = A_temp\n",
    "\n",
    "        gamma = np.zeros((kbar, 1))\n",
    "        gamma[0] = 1 - (1 - gamma_k) ** (1 / (b ** (kbar - 1)))\n",
    "\n",
    "        def bitget(number, position):\n",
    "\n",
    "            bi_number = bin(number)\n",
    "            bi_number = bi_number[2:]\n",
    "            if len(bi_number) >= position:\n",
    "\n",
    "                fn_output = bi_number[-position]\n",
    "            else:\n",
    "                fn_output = 0\n",
    "\n",
    "            return fn_output\n",
    "\n",
    "        for i in range(1, kbar):\n",
    "            gamma[i, 0] = 1 - (1 - gamma[0]) ** (b ** i)\n",
    "\n",
    "        gamma = gamma / 2\n",
    "        gamma = np.append(gamma, gamma, axis=1)\n",
    "        gamma[:, 0] = 1 - gamma[:, 0]\n",
    "        \n",
    "         #print(gamma[:,1])\n",
    "         #print(gamma[-1,1])\n",
    "\n",
    "        kbar1 = kbar + 1\n",
    "        kbar2 = 2 ** kbar\n",
    "\n",
    "        prob = np.ones((kbar2, 1))\n",
    "\n",
    "        for i in range(0, kbar2):\n",
    "            for m in range(1, kbar + 1):\n",
    "                prob[i, 0] = prob[i, 0] * gamma[kbar1 - m - 1, int(bitget(i, m))]\n",
    "\n",
    "        for i in range(0, 2 ** (kbar - 1)):\n",
    "            for j in range(i, 2 ** (kbar - 1)):\n",
    "                A[kbar2 - i - 1, j] = prob[kbar2 - int(A[i, j]) - 1, 0]\n",
    "                A[kbar2 - j - 1, i] = A[kbar2 - i - 1, j]\n",
    "                A[j, kbar2 - i - 1] = A[kbar2 - i - 1, j]\n",
    "                A[i, kbar2 - j - 1] = A[kbar2 - i - 1, j]\n",
    "\n",
    "                A[i, j] = prob[int(A[i, j]), 0]\n",
    "                A[j, i] = A[i, j]\n",
    "                A[kbar2 - i - 1, kbar2 - j - 1] = A[i, j]\n",
    "                A[kbar2 - j - 1, kbar2 - i - 1] = A[i, j]\n",
    "        return A, gamma\n",
    "\n",
    "    def gofm(m0, kbar):\n",
    "\n",
    "        m1 = 2 - m0\n",
    "        kbar2 = 2 ** kbar\n",
    "        g_m1 = list(range(0, kbar2))\n",
    "        for i in range(0, kbar2):\n",
    "            g = 1\n",
    "            for j in range(0, kbar):  # not req -1\n",
    "                if g_m1[i] & 2 ** j != 0:\n",
    "                    g = g * m1\n",
    "                else:\n",
    "                    g = g * m0\n",
    "            g_m1[i] = g\n",
    "\n",
    "        g_m = np.sqrt(g_m1)\n",
    "        return g_m\n",
    "\n",
    "    A, gamma = transition_mat(A_temp, b, gamma_k, kbar)\n",
    "    g_m = gofm(m0, kbar)\n",
    "    T = len(data)\n",
    "    pi_mat = np.zeros((T + 1, k2))\n",
    "    LLs = np.zeros((T,1))\n",
    "    pi_mat[0, :] = (1 / k2) * np.ones((1, k2))\n",
    "\n",
    "    # Likelihood Algorithm\n",
    "\n",
    "    pa = (2 * np.pi) ** (-0.5)\n",
    "\n",
    "    # g_m is binomial measure ?\n",
    "    g_m = np.array(g_m).reshape((1, len(g_m)))\n",
    "    s = np.matlib.repmat(sigma * g_m, T, 1)\n",
    "\n",
    "\n",
    "    data2 = np.array(data).reshape((len(data), 1))\n",
    "\n",
    "    w_t = np.matlib.repmat(data2, 1, k2)\n",
    "    w_t = np.divide(pa * np.e ** (-0.5 * np.power(np.divide(w_t, s), 2)), s)\n",
    "    w_t = w_t + 10 ** -16\n",
    "\n",
    "    for t in range(0, T):\n",
    "        piA = np.matmul(pi_mat[t, :], A)\n",
    "        C = np.multiply(w_t[t, :], piA)\n",
    "        ft = sum(C)\n",
    "\n",
    "        # stop div by zero if prob are too low\n",
    "        if ft == 0:\n",
    "            pi_mat[t + 1, 0] = 1\n",
    "        else:\n",
    "            pi_mat[t + 1, :] = np.divide(C, ft)\n",
    "\n",
    "        LLs[t] = np.log(np.dot(w_t[t, :], piA))\n",
    "\n",
    "    LL = -sum(LLs)\n",
    "\n",
    "    if np.isinf(LL):\n",
    "        print('Log-likelihood is inf. Probably due to all zeros in pi_mat.')\n",
    "\n",
    "    if len(args) == 4:\n",
    "\n",
    "        # prediction\n",
    "        t_predict = args[3]\n",
    "        vol = np.ones((t_predict,1))\n",
    "        vol = vol.astype(float)\n",
    "        state_now = pi_mat[-1 , :]\n",
    "        for t in range(0,t_predict):\n",
    "            vol[t,0] = sum(np.matmul(state_now, np.linalg.matrix_power(A, t+1)))*sigma\n",
    "\n",
    "        return vol\n",
    "\n",
    "    else:\n",
    "        return sum(LL)#+1/(2*gamma[-1,1])-1"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MSM_fitdata(data, kbar, LB ,UB, op_methods, startingvals):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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    "def MSM_fitdata(data, kbar, LB ,UB, op_methods, startingvals):\n",
    "    \"\"\"\n",
    "    Combine MSM_likelihood_new, MSM_starting_values, T_mat_Temp\n",
    "    :param data: Must be a column vector of a log return\n",
    "    from latest day [index0 : 1 Jan 1974] to today [index -1 : 1 Jan 2018]\n",
    "    multiply it with 100\n",
    "    :param kbar:\n",
    "    :param LB:\n",
    "    :param UB:\n",
    "    :param op_methods:\n",
    "    :param startingvals:\n",
    "    :return:\n",
    "    \"\"\"\n",
    "\n",
    "    input_param, LLS = MSM_starting_values(data, startingvals, kbar)\n",
    "        # print('LL = %8.4f' % LLS.loc[0, 'LL'])\n",
    "        \n",
    "     #input_param = startingvals\n",
    "    \n",
    "    # create a set of Parameters\n",
    "    params = Parameters()\n",
    "    params.add('m0', value=input_param[0], min=LB[0], max=UB[0])\n",
    "    params.add('b', value=input_param[1], min=LB[1], max=UB[1])\n",
    "    params.add('gamma_k', input_param[2], min=LB[2], max=UB[2])\n",
    "    params.add('sigma', value=input_param[3], min=LB[3], max=UB[3])\n",
    "\n",
    "    print(\"==========init params=========\")\n",
    "    for element in params:\n",
    "        print(element + \" = %8.4f\" % (params[element].value))\n",
    "\n",
    "\n",
    "\n",
    "    minner = Minimizer(MSM_likelihood_new, params, fcn_args=(kbar, data))\n",
    "    result = minner.minimize(method=op_methods)\n",
    "    \n",
    "\n",
    "    print(\"\\n\\n ==========fitted results==========\")\n",
    "    print('optimization method = ' + op_methods)\n",
    "    for element in result.params:\n",
    "        print(element + \" = %8.4f\" % (result.params[element].value))\n",
    "    print(\"\\n\")\n",
    "    # print('LLs = %8.4f' % (result.residual))\n",
    "    # print('AIC = %8.4f' % (result.aic))\n",
    "    # print('BIC = %8.4f' % (result.bic))\n",
    "\n",
    "    return result"
   ]
  },
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   "metadata": {},
   "source": [
    "## msm_fitseries(data, kbar, LB, UB, op_methods, startingvals, m, RV):\n",
    "    "
   ]
  },
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   "source": [
    "def msm_fitseries(data, kbar, LB, UB, op_methods, startingvals, m, RV):\n",
    "    \"\"\"\n",
    "     series of MSM_fitdata for calculate step-by-step\n",
    "    :param data: \n",
    "    :param kbar: \n",
    "    :param LB: \n",
    "    :param UB: \n",
    "    :param op_methods: OPTIMIZATION METHOD\n",
    "    :param startingvals: \n",
    "    :param m: numbers of days we try to estimate\n",
    "    :param RV: days to calculate RV\n",
    "    :return: \n",
    "    \"\"\"\n",
    "    output = df()\n",
    "    output[\"RV\"] = []\n",
    "    output[\"m0\"] = []\n",
    "    output[\"b\"] = []\n",
    "    output[\"gamma_k\"] = []\n",
    "    output[\"sigma\"] = []\n",
    "\n",
    "    for i in range(0, m):\n",
    "        print(\"round\" + str(i))\n",
    "        data2 = data[i:len(data) - m + i]\n",
    "        result = MSM_fitdata(data2, kbar, LB, UB, op_methods, startingvals)\n",
    "        re2 = MSM_likelihood_new(result.params, kbar, data2, RV)\n",
    "        output.loc[i, \"RV\"] = sum(re2) ** 2 * 100\n",
    "        for element in result.params:\n",
    "            output.loc[i, element] = result.params[element].value\n",
    "\n",
    "    return output"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## msm_averageparams(output, kbar, m, data, RV, LB , UB):\n",
    "    "
   ]
  },
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   "source": [
    "def msm_averageparams(output, kbar, m, data, RV, LB , UB):\n",
    "    \"\"\"\n",
    "    AVERAGE INPUT PARAMS for test robutness of model\n",
    "    :param output:\n",
    "    :param kbar:\n",
    "    :param m:\n",
    "    :param data:\n",
    "    :param RV:\n",
    "    :param LB:\n",
    "    :param UB:\n",
    "    :return:\n",
    "    \"\"\"\n",
    "    mean_o = output.mean()\n",
    "    params = Parameters()\n",
    "    params.add('m0', value=mean_o[1], min=LB[0], max=UB[0])\n",
    "    params.add('b', value=mean_o[2], min=LB[1], max=UB[1])\n",
    "    params.add('gamma_k', mean_o[3], min=LB[2], max=UB[2])\n",
    "    params.add('sigma', value=mean_o[4], min=LB[3], max=UB[3])\n",
    "\n",
    "    output_m = df()\n",
    "    output_m[\"RV\"] = []\n",
    "    output_m[\"m0\"] = []\n",
    "    output_m[\"b\"] = []\n",
    "    output_m[\"gamma_k\"] = []\n",
    "    output_m[\"sigma\"] = []\n",
    "\n",
    "    for i in range(0, m):\n",
    "        data2 = data[i:len(data) - m + i]\n",
    "        re2 = MSM_likelihood_new(params, kbar, data2, RV)\n",
    "        output_m.loc[i, \"RV\"] = sum(re2) ** 2 * 100\n",
    "        for element in params:\n",
    "            output_m.loc[i, element] = params[element].value\n",
    "\n",
    "    return output_m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## msm_plot"
   ]
  },
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   "source": [
    "def msm_plot(GVZ, output, m):\n",
    "    \"\"\"\n",
    "    plot quickly\n",
    "    :param GVZ:\n",
    "    :param output:\n",
    "    :param m:\n",
    "    :return:\n",
    "    \"\"\"\n",
    "\n",
    "    # GVZ = xls_data['GVZ']\n",
    "    GVZ_lastm = GVZ[::-1]\n",
    "    GVZ_lastm = GVZ_lastm.iloc[-m:]\n",
    "\n",
    "    plt.figure()\n",
    "    actual = plt.plot(range(0, m), GVZ_lastm, label='GVZ', color='red')\n",
    "    model = plt.plot(range(0, m), (output['RV']), label='MSM')\n",
    "\n",
    "    plt.title('Predict VOL actual(GVZ) vs forecast(model)')\n",
    "    plt.legend()\n",
    "\n",
    "    plt.figure()\n",
    "    plt.plot(range(0, m), output['m0'], label='m0')\n",
    "    plt.title('m0')\n",
    "    plt.legend()\n",
    "\n",
    "    plt.figure()\n",
    "    plt.plot(range(0, m), output['b'], label='b')\n",
    "    plt.title('b')\n",
    "    plt.legend()\n",
    "\n",
    "    plt.figure()\n",
    "    plt.plot(range(0, m), output['gamma_k'], label='gamma_k')\n",
    "    plt.title('gamma_k')\n",
    "    plt.legend()\n",
    "\n",
    "    plt.figure()\n",
    "    plt.plot(range(0, m), output['gamma_k'], label='gamma_k')\n",
    "    plt.title('gamma_k')\n",
    "    plt.legend()\n",
    "\n",
    "    plt.figure()\n",
    "    plt.plot(range(0, m), output['sigma'], label='sigma')\n",
    "    plt.title('sigma')\n",
    "    plt.legend()\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## linreg(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:03:51.084940Z",
     "start_time": "2018-02-28T14:03:51.053677Z"
    },
    "code_folding": [
     0
    ],
    "collapsed": true,
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "def linreg(x,y):\n",
    "    \"\"\"\n",
    "    Quick Regression\n",
    "    :param x:\n",
    "    :param y:\n",
    "    :return:\n",
    "    \"\"\"\n",
    "    # Create linear regression object\n",
    "    regr = linear_model.LinearRegression()\n",
    "\n",
    "    # Train the model using the training sets\n",
    "    regr.fit(x, y)\n",
    "\n",
    "    # The coefficients\n",
    "    print('Slope : ', sum(sum(regr.coef_)))\n",
    "    print('Intercept : ', sum(regr.intercept_))\n",
    "\n",
    "    # # The mean squared error\n",
    "    # print(\"Mean squared error: %.2f\"\n",
    "    #       % mean_squared_error(diabetes_y_test, diabetes_y_pred))\n",
    "    # # Explained variance score: 1 is perfect prediction\n",
    "    # print('Variance score: %.2f' % r2_score(diabetes_y_test, diabetes_y_pred))\n",
    "\n",
    "    return sum(sum(regr.coef_)), sum(regr.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## msm_vary_k_cal(data, vary, kbar_start, kbar_max, LB, UB, op_methods, startingvals, m, RVn):\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:03:51.131812Z",
     "start_time": "2018-02-28T14:03:51.084940Z"
    },
    "code_folding": [
     0
    ],
    "collapsed": true,
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "def msm_vary_k_cal(data, vary, kbar_start, kbar_max, LB, UB, op_methods, startingvals, m, RVn):\n",
    "    \"\"\"\n",
    "    calculation by vary kbar to see the effect of kbar\n",
    "    :param data:\n",
    "    :param vary: \"k\"\n",
    "    :param kbar_start:\n",
    "    :param kbar_max:\n",
    "    :param LB:\n",
    "    :param UB:\n",
    "    :param op_methods:\n",
    "    :param startingvals:\n",
    "    :param m:\n",
    "    :param RVn:\n",
    "    :return:\n",
    "    \"\"\"\n",
    "    RV = df()\n",
    "    m0 = df()\n",
    "    b = df()\n",
    "    gamma_k = df()\n",
    "    sigma = df()\n",
    "\n",
    "    for kbar in range(kbar_start, kbar_max):\n",
    "        # fit series\n",
    "        print(\"=====kbar = \" + str(kbar))\n",
    "        output = msm_fitseries(data, kbar, LB, UB, op_methods, startingvals, m, RVn)\n",
    "        RV[vary + str(kbar)] = output[\"RV\"]\n",
    "        m0[vary + str(kbar)] = output[\"m0\"]\n",
    "        b[vary + str(kbar)] = output[\"b\"]\n",
    "        gamma_k[vary + str(kbar)] = output[\"gamma_k\"]\n",
    "        sigma[vary + str(kbar)] = output[\"sigma\"]\n",
    "\n",
    "    text = 'MSM_vary_kbar'\n",
    "    namew = text + str(kbar_max) + \"_RV\" + str(RVn) + '_m' + str(m) + \".xlsx\"\n",
    "    writer = pd.ExcelWriter(\"\".join((date.today().strftime('%y%m%d'), namew)))\n",
    "    RV.to_excel(writer, 'RV')\n",
    "    m0.to_excel(writer, 'm0')\n",
    "    b.to_excel(writer, 'b')\n",
    "    gamma_k.to_excel(writer, 'gamma_k')\n",
    "    sigma.to_excel(writer, 'sigma')\n",
    "    print(\"\".join((date.today().strftime('%y%m%d'), namew)))\n",
    "    writer.save()\n",
    "\n",
    "    #frequency = 2500  # Set Frequency To 2500 Hertz\n",
    "    #duration = 1000  # Set Duration To 1000 ms == 1 second\n",
    "    #winsound.Beep(frequency, duration)\n",
    "\n",
    "    return RV, m0, b, gamma_k, sigma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## msm_vary_k_plot(GVZ, m=20, *args):\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:03:51.209944Z",
     "start_time": "2018-02-28T14:03:51.131812Z"
    },
    "code_folding": [
     0
    ],
    "collapsed": true,
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "def msm_vary_k_plot(GVZ, m=20, *args):\n",
    "\n",
    "    def label_plot(m, x, LA):\n",
    "        for LAs in LA:\n",
    "            plt.plot(range(0, m), x[LAs], label=LAs)\n",
    "\n",
    "    if len(args) == 1:\n",
    "        xls = pd.ExcelFile(args[0])\n",
    "        RV = pd.read_excel(xls, 'RV')\n",
    "        m0 = pd.read_excel(xls, 'm0')\n",
    "        b = pd.read_excel(xls, 'b')\n",
    "        gamma_k = pd.read_excel(xls, 'gamma_k')\n",
    "        sigma = pd.read_excel(xls, 'sigma')\n",
    "\n",
    "    elif len(args) == 5:\n",
    "        RV = args[0]\n",
    "        m0 = args[1]\n",
    "        b = args[2]\n",
    "        gamma_k = args[3]\n",
    "        sigma = args[4]\n",
    "\n",
    "    GVZ_lastm = GVZ.iloc[-m:]\n",
    "\n",
    "    rcParams['figure.figsize'] = 5, 25\n",
    "\n",
    "    LA = m0.columns.tolist()\n",
    "\n",
    "    plt.subplot(511)\n",
    "    actual = plt.plot(range(0, m), GVZ_lastm, label='GVZ', color='red')\n",
    "    label_plot(m, RV, LA)\n",
    "    plt.title('Predict VOL actual(GVZ) vs forecast(model)')\n",
    "    plt.legend()\n",
    "\n",
    "    plt.subplot(512)\n",
    "    label_plot(m, m0, LA)\n",
    "    plt.title('m0')\n",
    "    plt.legend()\n",
    "\n",
    "    plt.subplot(513)\n",
    "    label_plot(m, b, LA)\n",
    "    plt.title('b')\n",
    "    plt.legend()\n",
    "\n",
    "    plt.subplot(514)\n",
    "    label_plot(m, gamma_k, LA)\n",
    "    plt.title('gamma_k')\n",
    "    plt.legend()\n",
    "\n",
    "    plt.subplot(515)\n",
    "    label_plot(m, sigma, LA)\n",
    "    plt.title('sigma')\n",
    "    plt.legend()\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MSM_likelihood_wantto_forecast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:09:07.576295Z",
     "start_time": "2018-02-28T14:09:07.326026Z"
    },
    "code_folding": [],
    "collapsed": true,
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "def MSM_likelihood_wantto_forecast(*args):\n",
    "    \"\"\"\n",
    "    calculate LL for 3 cases (depend on number of input)\n",
    "    :param args:\n",
    "    :return:\n",
    "    \"\"\"\n",
    "\n",
    "    if len(args) ==3 :\n",
    "        # choose starting val\n",
    "        inp = args[0]\n",
    "        kbar = args[1]\n",
    "        data = args[2]\n",
    "        m0 = inp['m0'].value\n",
    "        b = inp['b'].value\n",
    "        gamma_k = inp['gamma_k'].value\n",
    "        sigma = inp['sigma'].value\n",
    "\n",
    "    elif len(args) == 4 :\n",
    "        # prediction\n",
    "        inp = args[0]\n",
    "        kbar = args[1]\n",
    "        data = args[2]\n",
    "        m0 = inp['m0'].value\n",
    "        b = inp['b'].value\n",
    "        gamma_k = inp['gamma_k'].value\n",
    "        sigma = inp['sigma'].value\n",
    "        \n",
    "\n",
    "    A_temp = T_mat_temp(kbar)\n",
    "    k2 = 2 ** kbar\n",
    "\n",
    "    def transition_mat(A_temp, b, gamma_k, kbar):\n",
    "        A = A_temp\n",
    "\n",
    "        gamma = np.zeros((kbar, 1))\n",
    "        gamma[0] = 1 - (1 - gamma_k) ** (1 / (b ** (kbar - 1)))\n",
    "\n",
    "        def bitget(number, position):\n",
    "\n",
    "            bi_number = bin(number)\n",
    "            bi_number = bi_number[2:]\n",
    "            if len(bi_number) >= position:\n",
    "\n",
    "                fn_output = bi_number[-position]\n",
    "            else:\n",
    "                fn_output = 0\n",
    "\n",
    "            return fn_output\n",
    "\n",
    "        for i in range(1, kbar):\n",
    "            gamma[i, 0] = 1 - (1 - gamma[0]) ** (b ** i)\n",
    "\n",
    "        gamma = gamma / 2\n",
    "        gamma = np.append(gamma, gamma, axis=1)\n",
    "        gamma[:, 0] = 1 - gamma[:, 0]\n",
    "\n",
    "        kbar1 = kbar + 1\n",
    "        kbar2 = 2 ** kbar\n",
    "\n",
    "        prob = np.ones((kbar2, 1))\n",
    "\n",
    "        for i in range(0, kbar2):\n",
    "            for m in range(1, kbar + 1):\n",
    "                prob[i, 0] = prob[i, 0] * gamma[kbar1 - m - 1, int(bitget(i, m))]\n",
    "\n",
    "        for i in range(0, 2 ** (kbar - 1)):\n",
    "            for j in range(i, 2 ** (kbar - 1)):\n",
    "                A[kbar2 - i - 1, j] = prob[kbar2 - int(A[i, j]) - 1, 0]\n",
    "                A[kbar2 - j - 1, i] = A[kbar2 - i - 1, j]\n",
    "                A[j, kbar2 - i - 1] = A[kbar2 - i - 1, j]\n",
    "                A[i, kbar2 - j - 1] = A[kbar2 - i - 1, j]\n",
    "\n",
    "                A[i, j] = prob[int(A[i, j]), 0]\n",
    "                A[j, i] = A[i, j]\n",
    "                A[kbar2 - i - 1, kbar2 - j - 1] = A[i, j]\n",
    "                A[kbar2 - j - 1, kbar2 - i - 1] = A[i, j]\n",
    "        return A\n",
    "\n",
    "    def gofm(m0, kbar):\n",
    "\n",
    "        m1 = 2 - m0\n",
    "        kbar2 = 2 ** kbar\n",
    "        g_m1 = list(range(0, kbar2))\n",
    "        for i in range(0, kbar2):\n",
    "            g = 1\n",
    "            for j in range(0, kbar):  # not req -1\n",
    "                if g_m1[i] & 2 ** j != 0:\n",
    "                    g = g * m1\n",
    "                else:\n",
    "                    g = g * m0\n",
    "            g_m1[i] = g\n",
    "\n",
    "        g_m = np.sqrt(g_m1)\n",
    "        return g_m\n",
    "\n",
    "    A = transition_mat(A_temp, b, gamma_k, kbar)\n",
    "    g_m = gofm(m0, kbar)\n",
    "    T = len(data)\n",
    "    pi_mat = np.zeros((T + 1, k2))\n",
    "    LLs = np.zeros((T,1))\n",
    "    pi_mat[0, :] = (1 / k2) * np.ones((1, k2))\n",
    "\n",
    "    # Likelihood Algorithm\n",
    "\n",
    "    pa = (2 * np.pi) ** (-0.5)\n",
    "\n",
    "    # g_m is binomial measure ?\n",
    "    g_m = np.array(g_m).reshape((1, len(g_m)))\n",
    "    s = np.matlib.repmat(sigma * g_m, T, 1)\n",
    "\n",
    "\n",
    "    data2 = np.array(data).reshape((len(data), 1))\n",
    "\n",
    "    w_t = np.matlib.repmat(data2, 1, k2)\n",
    "    w_t = np.divide(pa * np.e ** (-0.5 * np.power(np.divide(w_t, s), 2)), s)\n",
    "    w_t = w_t + 10 ** -16\n",
    "\n",
    "    for t in range(0, T):\n",
    "        piA = np.matmul(pi_mat[t, :], A)\n",
    "        C = np.multiply(w_t[t, :], piA)\n",
    "        ft = sum(C)\n",
    "\n",
    "        # stop div by zero if prob are too low\n",
    "        if ft == 0:\n",
    "            pi_mat[t + 1, :] = (1 / k2) * np.ones((1, k2))\n",
    "            print(\"!!!!!\")\n",
    "        else:\n",
    "            pi_mat[t + 1, :] = np.divide(C, ft)\n",
    "\n",
    "        LLs[t] = np.log(np.dot(w_t[t, :], piA))\n",
    "\n",
    "    LL = -sum(LLs)\n",
    "\n",
    "    if np.isinf(LL):\n",
    "        print('Log-likelihood is inf. Probably due to all zeros in pi_mat.')\n",
    "\n",
    "    if len(args) == 4:\n",
    "\n",
    "        # provide ingrdents for forecast\n",
    "        \n",
    "        return pi_mat, A, sigma, s\n",
    "\n",
    "    else:\n",
    "        return sum(LL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TEST FIT_PARAMS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## INPUT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:06:04.973905Z",
     "start_time": "2018-02-28T14:06:03.691413Z"
    },
    "collapsed": true,
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "filename = 'fed_data.xlsx'\n",
    "xls = pd.ExcelFile(filename)\n",
    "CA_raw = pd.read_excel(xls, 'CA')\n",
    "DM_raw = pd.read_excel(xls, 'DM')\n",
    "JA_raw = pd.read_excel(xls, 'JA')\n",
    "UK_raw = pd.read_excel(xls, 'UK')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### construct a reaw data matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:06:05.098426Z",
     "start_time": "2018-02-28T14:06:05.067174Z"
    },
    "code_folding": [
     0
    ],
    "collapsed": true,
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "def T3(dum_data, Table3_Currency_Vol, row):\n",
    "    returns = 100*np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "    subperiod = 4\n",
    "    Table3_Currency_Vol.loc[row,'Entire'] = float(np.std(returns))\n",
    "    for i in range(0,subperiod):\n",
    "        sub_data = dum_data['Column2']\n",
    "        #print('i = ' + str(i))\n",
    "        #print('from : ',int(np.floor(i*len(returns)/subperiod)))\n",
    "        #print('to   : ',int(np.floor((i+1)*len(returns)/subperiod)))\n",
    "        sub_data = sub_data.iloc[int(np.floor(i*len(returns)/subperiod)):int(np.floor((i+1)*len(returns)/subperiod))]\n",
    "        returns2 = 100*np.log(1+sub_data.pct_change().dropna())\n",
    "        Table3_Currency_Vol.iloc[row,i+1] = float(np.std(returns2))\n",
    "        \n",
    "    return Table3_Currency_Vol\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:06:11.006901Z",
     "start_time": "2018-02-28T14:06:10.928769Z"
    },
    "deletable": false,
    "editable": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Entire</th>\n",
       "      <th>Sub1</th>\n",
       "      <th>Sub2</th>\n",
       "      <th>Sub3</th>\n",
       "      <th>Sub4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.664101</td>\n",
       "      <td>0.586819</td>\n",
       "      <td>0.716642</td>\n",
       "      <td>0.708206</td>\n",
       "      <td>0.635449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.656566</td>\n",
       "      <td>0.544619</td>\n",
       "      <td>0.639886</td>\n",
       "      <td>0.645119</td>\n",
       "      <td>0.775137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.606847</td>\n",
       "      <td>0.485806</td>\n",
       "      <td>0.724471</td>\n",
       "      <td>0.699407</td>\n",
       "      <td>0.472817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.274376</td>\n",
       "      <td>0.220132</td>\n",
       "      <td>0.254553</td>\n",
       "      <td>0.284356</td>\n",
       "      <td>0.326698</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Entire      Sub1      Sub2      Sub3      Sub4\n",
       "0  0.664101  0.586819  0.716642  0.708206  0.635449\n",
       "1  0.656566  0.544619  0.639886  0.645119  0.775137\n",
       "2  0.606847  0.485806  0.724471  0.699407  0.472817\n",
       "3  0.274376  0.220132  0.254553  0.284356  0.326698"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Table3_Currency_Vol = df()\n",
    "Table3_Currency_Vol['Entire']=[]\n",
    "Table3_Currency_Vol['Sub1']=[]\n",
    "Table3_Currency_Vol['Sub2']=[]\n",
    "Table3_Currency_Vol['Sub3']=[]\n",
    "Table3_Currency_Vol['Sub4']=[]\n",
    "\n",
    "raw = [DM_raw, JA_raw, UK_raw, CA_raw]\n",
    "for row in range(0, len(raw)):\n",
    "    Table3_Currency_Vol = T3(raw[row], Table3_Currency_Vol, row)\n",
    "Table3_Currency_Vol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### plot to see data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T12:38:00.182997Z",
     "start_time": "2018-02-25T12:37:59.119974Z"
    },
    "deletable": false,
    "editable": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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aew8A+znnBznnpQC+BXCjCe0SBEEQOjBDsDcCICyikO/eRhAEQVhAyJynjLGx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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x236b8873128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Tz/tz8dR3+/DPnw9oO5DM76Een96MU4W6Xdi+21l9oSmrqMLbqw973V/t8ody74J9eWVF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\njdcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x236b89f8f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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D4QseJ/U9/Pku/WzQ6Lcsr+CYtlT6uIephD2AlN2JxKkrUFDsnB2y888r2Jl9pcp7Gw9f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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x236b89f8f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7TmgyYd34wTJ888/ulshrJGX0rSrRxEZQm0mtD6d4FOnvFPSUhXUDTkoJbidm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\nCZlNT5MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x236b89f8fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# rcParams['figure.figsize'] = 5, 10\n",
    "\n",
    "for row in range(0, len(raw)):\n",
    "    dum_data = raw[row]\n",
    "    returns = 100*np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "    a = returns.to_frame()\n",
    "    a.plot()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OUTPUT"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Construct a output dataframe for store hard working parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T12:39:14.901979Z",
     "start_time": "2018-02-25T12:39:14.870468Z"
    },
    "collapsed": true,
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "output = df()\n",
    "output[\"m0\"] = []\n",
    "output[\"b\"] = []\n",
    "output[\"gamma_k\"]=[]\n",
    "output[\"sigma\"] = []\n",
    "output[\"LL\"] = []\n",
    "result = []\n",
    "\n",
    "startingvals = []#[1.2, 1.2, 0.5 , 1.2 ]\n",
    "LB = [1, 1, 0.001, 0.0001]\n",
    "UB = [1.99, 50, 0.99999, 50]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### DM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-19T10:57:18.317606Z",
     "start_time": "2018-02-19T10:30:37.710453Z"
    },
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         LL    b     g        m sigma\n",
      "0   5924.15  1.5   0.1  1.66418   NaN\n",
      "1   5924.15    3   0.1  1.66418   NaN\n",
      "2   5924.15    6   0.1  1.66418   NaN\n",
      "3   5924.15   20   0.1  1.66418   NaN\n",
      "4   6029.55  1.5   0.5  1.74141   NaN\n",
      "5   6029.55    3   0.5  1.74141   NaN\n",
      "6   6029.55    6   0.5  1.74141   NaN\n",
      "7   6029.55   20   0.5  1.74141   NaN\n",
      "8   6135.42  1.5  0.99  1.73377   NaN\n",
      "9   6135.42    3  0.99  1.73377   NaN\n",
      "10  6135.42    6  0.99  1.73377   NaN\n",
      "11  6135.42   20  0.99  1.73377   NaN\n",
      "==========init params=========\n",
      "m0 =   1.6642\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6642\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.6541\n",
      "b =   1.5000\n",
      "gamma_k =   0.0747\n",
      "sigma =   0.6819\n",
      "\n",
      "\n",
      "         LL    b          g        m sigma\n",
      "0   5794.83  1.5  0.0747172  1.57793   NaN\n",
      "1   5794.83  1.5  0.0747172  1.57793   NaN\n",
      "2   5794.83  1.5  0.0747172  1.57793   NaN\n",
      "3   5794.83  1.5  0.0747172  1.57793   NaN\n",
      "4   5959.69  1.5   0.532359  1.62232   NaN\n",
      "5   5959.69  1.5   0.532359  1.62232   NaN\n",
      "6   5959.69  1.5   0.532359  1.62232   NaN\n",
      "7   5959.69  1.5   0.532359  1.62232   NaN\n",
      "8   6098.13  1.5       0.99  1.60686   NaN\n",
      "9   6098.13  1.5       0.99  1.60686   NaN\n",
      "10  6098.13  1.5       0.99  1.60686   NaN\n",
      "11  6098.13  1.5       0.99  1.60686   NaN\n",
      "==========init params=========\n",
      "m0 =   1.5779\n",
      "b =   1.5000\n",
      "gamma_k =   0.0747\n",
      "sigma =   0.6819\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.5899\n",
      "b =   8.0165\n",
      "gamma_k =   0.1068\n",
      "sigma =   0.6506\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   5742.48   5.8443  0.106826  1.53916   NaN\n",
      "1   5743.16  8.01646  0.106826  1.54353   NaN\n",
      "2   5745.42  3.67215  0.106826  1.52949   NaN\n",
      "3   5748.58  8.01646  0.548413  1.54262   NaN\n",
      "4   5761.88   5.8443  0.548413  1.53308   NaN\n",
      "5   5768.66      1.5  0.106826  1.50806   NaN\n",
      "6   5797.98  3.67215  0.548413   1.5234   NaN\n",
      "7   5832.22  8.01646      0.99  1.53146   NaN\n",
      "8   5876.75   5.8443      0.99  1.52915   NaN\n",
      "9   5925.43      1.5  0.548413  1.51918   NaN\n",
      "10  5963.16  3.67215      0.99   1.5232   NaN\n",
      "11  6084.62      1.5      0.99   1.4986   NaN\n",
      "==========init params=========\n",
      "m0 =   1.5392\n",
      "b =   5.8443\n",
      "gamma_k =   0.1068\n",
      "sigma =   0.6506\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.5546\n",
      "b =  21.9143\n",
      "gamma_k =   0.6725\n",
      "sigma =   0.6003\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   5717.63  8.30478  0.672529   1.4891   NaN\n",
      "1   5718.18  15.1096  0.831264  1.49986   NaN\n",
      "2    5721.7  8.30478  0.831264  1.48425   NaN\n",
      "3   5722.63  15.1096  0.672529  1.50411   NaN\n",
      "4   5725.01  21.9143  0.831264  1.51143   NaN\n",
      "5   5726.66  21.9143      0.99   1.4986   NaN\n",
      "6   5726.94  15.1096      0.99  1.48759   NaN\n",
      "7   5732.49  21.9143  0.672529  1.52361   NaN\n",
      "8   5743.15  8.30478      0.99  1.48111   NaN\n",
      "9   5947.22      1.5  0.672529  1.44344   NaN\n",
      "10  6006.26      1.5  0.831264  1.43817   NaN\n",
      "11  6097.01      1.5      0.99   1.4184   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4891\n",
      "b =   8.3048\n",
      "gamma_k =   0.6725\n",
      "sigma =   0.6003\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.4915\n",
      "b =  10.4203\n",
      "gamma_k =   0.7135\n",
      "sigma =   0.5716\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   5711.67  7.44686  0.713536  1.46605   NaN\n",
      "1   5713.05  7.44686  0.851768  1.45903   NaN\n",
      "2    5713.3  10.4203  0.851768  1.47689   NaN\n",
      "3   5714.25  10.4203  0.713536  1.47954   NaN\n",
      "4   5716.69  4.47343  0.713536  1.43083   NaN\n",
      "5      5717  7.44686      0.99  1.44136   NaN\n",
      "6    5718.4  10.4203      0.99  1.46041   NaN\n",
      "7    5721.7  4.47343  0.851768  1.42902   NaN\n",
      "8   5748.84  4.47343      0.99  1.42588   NaN\n",
      "9   5945.11      1.5  0.713536  1.39672   NaN\n",
      "10  6004.85      1.5  0.851768  1.39217   NaN\n",
      "11     6110      1.5      0.99  1.37371   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4660\n",
      "b =   7.4469\n",
      "gamma_k =   0.7135\n",
      "sigma =   0.5716\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.4619\n",
      "b =   7.8867\n",
      "gamma_k =   0.7506\n",
      "sigma =   0.5117\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   5708.24  5.75778  0.870317  1.41686   NaN\n",
      "1   5710.19  5.75778      0.99  1.41541   NaN\n",
      "2   5710.51  5.75778  0.750633  1.41764   NaN\n",
      "3   5711.05  7.88667      0.99  1.42246   NaN\n",
      "4    5714.5  3.62889  0.750633  1.40295   NaN\n",
      "5   5716.52  7.88667  0.870317  1.42748   NaN\n",
      "6   5716.94  7.88667  0.750633  1.46487   NaN\n",
      "7   5721.03  3.62889  0.870317  1.40125   NaN\n",
      "8   5749.43  3.62889      0.99  1.39694   NaN\n",
      "9   5997.34      1.5  0.750633  1.36755   NaN\n",
      "10  6069.34      1.5  0.870317  1.36277   NaN\n",
      "11  6212.19      1.5      0.99  1.34459   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4169\n",
      "b =   5.7578\n",
      "gamma_k =   0.8703\n",
      "sigma =   0.5117\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.4129\n",
      "b =   5.1603\n",
      "gamma_k =   0.8583\n",
      "sigma =   0.5377\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   5704.71  3.94019  0.924136  1.37757   NaN\n",
      "1   5705.02  3.94019  0.858273  1.38006   NaN\n",
      "2   5706.25  5.16029      0.99  1.38429   NaN\n",
      "3   5709.09  3.94019      0.99  1.37485   NaN\n",
      "4    5709.6  5.16029  0.924136  1.39366   NaN\n",
      "5   5712.42  5.16029  0.858273  1.40555   NaN\n",
      "6   5720.89   2.7201  0.858273  1.36041   NaN\n",
      "7   5727.88   2.7201  0.924136  1.35941   NaN\n",
      "8   5751.34   2.7201      0.99   1.3585   NaN\n",
      "9    5960.3      1.5  0.858273  1.33878   NaN\n",
      "10  6005.53      1.5  0.924136  1.33597   NaN\n",
      "11   6098.2      1.5      0.99  1.32571   NaN\n",
      "==========init params=========\n",
      "m0 =   1.3776\n",
      "b =   3.9402\n",
      "gamma_k =   0.9241\n",
      "sigma =   0.5377\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.3798\n",
      "b =   4.1176\n",
      "gamma_k =   0.9315\n",
      "sigma =   0.5467\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   5704.87  3.24509  0.960766  1.35102   NaN\n",
      "1   5705.05  3.24509  0.931533  1.35276   NaN\n",
      "2   5706.51  3.24509      0.99  1.34866   NaN\n",
      "3   5707.94  4.11763      0.99  1.36395   NaN\n",
      "4   5710.14  4.11763  0.960766  1.37167   NaN\n",
      "5   5710.81  4.11763  0.931533  1.38613   NaN\n",
      "6   5724.83  2.37254  0.931533  1.33386   NaN\n",
      "7   5730.61  2.37254  0.960766  1.33343   NaN\n",
      "8   5744.89  2.37254      0.99  1.33309   NaN\n",
      "9    5948.8      1.5  0.931533  1.31801   NaN\n",
      "10  5978.24      1.5  0.960766  1.31627   NaN\n",
      "11  6033.54      1.5      0.99  1.31135   NaN\n",
      "==========init params=========\n",
      "m0 =   1.3510\n",
      "b =   3.2451\n",
      "gamma_k =   0.9608\n",
      "sigma =   0.5467\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.3527\n",
      "b =   3.3817\n",
      "gamma_k =   0.9737\n",
      "sigma =   0.5504\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   5705.66   2.7545  0.973716  1.32777   NaN\n",
      "1   5705.99   2.7545  0.981858  1.32708   NaN\n",
      "2   5706.77   2.7545      0.99  1.32622   NaN\n",
      "3   5707.76  3.38175      0.99  1.34129   NaN\n",
      "4    5708.1  3.38175  0.981858  1.34406   NaN\n",
      "5   5708.28  3.38175  0.973716  1.34666   NaN\n",
      "6    5733.1  2.12725  0.973716  1.31275   NaN\n",
      "7   5736.89  2.12725  0.981858  1.31267   NaN\n",
      "8   5742.95  2.12725      0.99  1.31262   NaN\n",
      "9   5942.38      1.5  0.973716    1.301   NaN\n",
      "10  5957.16      1.5  0.981858  1.30018   NaN\n",
      "11  5978.51      1.5      0.99  1.29873   NaN\n",
      "==========init params=========\n",
      "m0 =   1.3278\n",
      "b =   2.7545\n",
      "gamma_k =   0.9737\n",
      "sigma =   0.5504\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.3306\n",
      "b =   2.8501\n",
      "gamma_k =   0.9729\n",
      "sigma =   0.5601\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   5706.02  2.40006  0.972934  1.30857   NaN\n",
      "1   5706.13   2.8501      0.99   1.3213   NaN\n",
      "2   5706.21   2.8501  0.981467  1.32392   NaN\n",
      "3   5706.29   2.8501  0.972934   1.3261   NaN\n",
      "4    5706.5  2.40006  0.981467  1.30782   NaN\n",
      "5    5707.5  2.40006      0.99  1.30685   NaN\n",
      "6   5731.06  1.95003  0.972934  1.29543   NaN\n",
      "7   5734.75  1.95003  0.981467  1.29537   NaN\n",
      "8   5740.77  1.95003      0.99  1.29536   NaN\n",
      "9   5885.41      1.5  0.972934  1.28852   NaN\n",
      "10  5898.92      1.5  0.981467  1.28821   NaN\n",
      "11  5919.08      1.5      0.99  1.28748   NaN\n",
      "==========init params=========\n",
      "m0 =   1.3086\n",
      "b =   2.4001\n",
      "gamma_k =   0.9729\n",
      "sigma =   0.5601\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.3257\n",
      "b =   2.7025\n",
      "gamma_k =   0.9589\n",
      "sigma =   0.6432\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>m0</th>\n",
       "      <th>b</th>\n",
       "      <th>gamma_k</th>\n",
       "      <th>sigma</th>\n",
       "      <th>LL</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.654133</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>0.074717</td>\n",
       "      <td>0.681917</td>\n",
       "      <td>5920.855214</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.589895</td>\n",
       "      <td>8.016456</td>\n",
       "      <td>0.106826</td>\n",
       "      <td>0.650560</td>\n",
       "      <td>5782.955933</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.554623</td>\n",
       "      <td>21.914346</td>\n",
       "      <td>0.672529</td>\n",
       "      <td>0.600255</td>\n",
       "      <td>5731.776138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.491546</td>\n",
       "      <td>10.420285</td>\n",
       "      <td>0.713536</td>\n",
       "      <td>0.571605</td>\n",
       "      <td>5715.300200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.461936</td>\n",
       "      <td>7.886674</td>\n",
       "      <td>0.750633</td>\n",
       "      <td>0.511672</td>\n",
       "      <td>5708.240226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.412923</td>\n",
       "      <td>5.160288</td>\n",
       "      <td>0.858273</td>\n",
       "      <td>0.537734</td>\n",
       "      <td>5706.903687</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.379843</td>\n",
       "      <td>4.117634</td>\n",
       "      <td>0.931533</td>\n",
       "      <td>0.546732</td>\n",
       "      <td>5704.470829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.352666</td>\n",
       "      <td>3.381746</td>\n",
       "      <td>0.973716</td>\n",
       "      <td>0.550389</td>\n",
       "      <td>5704.765369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.330602</td>\n",
       "      <td>2.850096</td>\n",
       "      <td>0.972934</td>\n",
       "      <td>0.560066</td>\n",
       "      <td>5705.342737</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.325676</td>\n",
       "      <td>2.702472</td>\n",
       "      <td>0.958863</td>\n",
       "      <td>0.643250</td>\n",
       "      <td>5705.085364</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         m0          b   gamma_k     sigma           LL\n",
       "0  1.654133   1.500000  0.074717  0.681917  5920.855214\n",
       "1  1.589895   8.016456  0.106826  0.650560  5782.955933\n",
       "2  1.554623  21.914346  0.672529  0.600255  5731.776138\n",
       "3  1.491546  10.420285  0.713536  0.571605  5715.300200\n",
       "4  1.461936   7.886674  0.750633  0.511672  5708.240226\n",
       "5  1.412923   5.160288  0.858273  0.537734  5706.903687\n",
       "6  1.379843   4.117634  0.931533  0.546732  5704.470829\n",
       "7  1.352666   3.381746  0.973716  0.550389  5704.765369\n",
       "8  1.330602   2.850096  0.972934  0.560066  5705.342737\n",
       "9  1.325676   2.702472  0.958863  0.643250  5705.085364"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "op_methods = 'slsqp'\n",
    "row = 0\n",
    "dum_data = raw[row]\n",
    "returns = np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "a = returns.to_frame()\n",
    "data = a['Column2']*100\n",
    "data2 = data#[::-1]\n",
    "startingvals = []\n",
    "\n",
    "for i in range(0,10):\n",
    "    kbar = i+1\n",
    "    if kbar >1 and bool(result):\n",
    "        startingvals = [result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value]\n",
    "    result = MSM_fitdata(data, kbar, LB ,UB,op_methods, startingvals)\n",
    "    re2 = MSM_likelihood_new(result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value,  kbar, data2)\n",
    "    output.loc[i,\"LL\"] = re2\n",
    "    for element in result.params:\n",
    "        output.loc[i,element] = result.params[element].value\n",
    "        \n",
    "writer = pd.ExcelWriter('Output'.join((date.today().strftime('%y%m%d'),op_methods+'DMvaryk.xlsx')))\n",
    "output.to_excel(writer, 'Sheet1')\n",
    "writer.save()\n",
    "        \n",
    "output  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### JPY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-19T11:37:09.291917Z",
     "start_time": "2018-02-19T11:06:27.800294Z"
    },
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         LL    b     g        m sigma\n",
      "0   6474.43  1.5   0.1  1.75145   NaN\n",
      "1   6474.43    3   0.1  1.75145   NaN\n",
      "2   6474.43    6   0.1  1.75145   NaN\n",
      "3   6474.43   20   0.1  1.75145   NaN\n",
      "4   6506.28  1.5   0.5  1.79999   NaN\n",
      "5   6506.28    3   0.5  1.79999   NaN\n",
      "6   6506.28    6   0.5  1.79999   NaN\n",
      "7   6506.28   20   0.5  1.79999   NaN\n",
      "8   6657.16  1.5  0.99  1.79999   NaN\n",
      "9   6657.16    3  0.99  1.79999   NaN\n",
      "10  6657.16    6  0.99  1.79999   NaN\n",
      "11  6657.16   20  0.99  1.79999   NaN\n",
      "==========init params=========\n",
      "m0 =   1.7514\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6566\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.7969\n",
      "b =   1.5000\n",
      "gamma_k =   0.1989\n",
      "sigma =   0.6298\n",
      "\n",
      "\n",
      "         LL    b         g        m sigma\n",
      "0   6198.81  1.5  0.198939  1.71102   NaN\n",
      "1   6198.81  1.5  0.198939  1.71102   NaN\n",
      "2   6198.81  1.5  0.198939  1.71102   NaN\n",
      "3   6198.81  1.5  0.198939  1.71102   NaN\n",
      "4   6368.15  1.5  0.594469  1.71573   NaN\n",
      "5   6368.15  1.5  0.594469  1.71573   NaN\n",
      "6   6368.15  1.5  0.594469  1.71573   NaN\n",
      "7   6368.15  1.5  0.594469  1.71573   NaN\n",
      "8    6568.8  1.5      0.99  1.67682   NaN\n",
      "9    6568.8  1.5      0.99  1.67682   NaN\n",
      "10   6568.8  1.5      0.99  1.67682   NaN\n",
      "11   6568.8  1.5      0.99  1.67682   NaN\n",
      "==========init params=========\n",
      "m0 =   1.7110\n",
      "b =   1.5000\n",
      "gamma_k =   0.1989\n",
      "sigma =   0.6298\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.7761\n",
      "b =  50.0000\n",
      "gamma_k =   0.3261\n",
      "sigma =   0.5430\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   5963.09  17.6667  0.326086  1.68829   NaN\n",
      "1   5968.21  17.6667  0.658043  1.68934   NaN\n",
      "2   5972.59  33.8333  0.658043  1.68323   NaN\n",
      "3   5978.96  33.8333  0.326086  1.68916   NaN\n",
      "4   5980.24       50      0.99  1.69085   NaN\n",
      "5   5983.79       50  0.658043  1.68021   NaN\n",
      "6   5991.43  33.8333      0.99  1.69535   NaN\n",
      "7   5992.22       50  0.326086  1.69033   NaN\n",
      "8   6043.31  17.6667      0.99  1.69295   NaN\n",
      "9   6188.09      1.5  0.326086   1.6467   NaN\n",
      "10  6394.62      1.5  0.658043  1.60796   NaN\n",
      "11  6645.14      1.5      0.99  1.54692   NaN\n",
      "==========init params=========\n",
      "m0 =   1.6883\n",
      "b =  17.6667\n",
      "gamma_k =   0.3261\n",
      "sigma =   0.5430\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.6930\n",
      "b =  12.4571\n",
      "gamma_k =   0.3119\n",
      "sigma =   0.5656\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   5913.76  12.4571  0.650972  1.65684   NaN\n",
      "1   5915.08  8.80472  0.650972  1.64714   NaN\n",
      "2   5930.03  8.80472  0.311943  1.67402   NaN\n",
      "3   5934.15  5.15236  0.311943  1.64253   NaN\n",
      "4   5934.39  12.4571  0.311943  1.68262   NaN\n",
      "5   5939.31  12.4571      0.99  1.62725   NaN\n",
      "6   5945.58  5.15236  0.650972   1.6286   NaN\n",
      "7   5967.45  8.80472      0.99   1.6233   NaN\n",
      "8   6069.35  5.15236      0.99  1.60041   NaN\n",
      "9   6108.83      1.5  0.311943   1.5797   NaN\n",
      "10  6294.61      1.5  0.650972  1.55083   NaN\n",
      "11  6565.61      1.5      0.99  1.49463   NaN\n",
      "==========init params=========\n",
      "m0 =   1.6568\n",
      "b =  12.4571\n",
      "gamma_k =   0.6510\n",
      "sigma =   0.5656\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.6540\n",
      "b =  15.5850\n",
      "gamma_k =   0.6974\n",
      "sigma =   0.4619\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   5887.43    10.89  0.843691  1.58338   NaN\n",
      "1   5887.51  6.19499  0.697383  1.58433   NaN\n",
      "2   5888.21    10.89      0.99  1.58664   NaN\n",
      "3   5890.91   15.585      0.99  1.58289   NaN\n",
      "4   5891.33  6.19499  0.843691  1.58298   NaN\n",
      "5    5896.1    10.89  0.697383  1.58322   NaN\n",
      "6   5900.91   15.585  0.843691   1.5816   NaN\n",
      "7   5912.12   15.585  0.697383  1.65069   NaN\n",
      "8    5927.6  6.19499      0.99  1.57129   NaN\n",
      "9   6413.38      1.5  0.697383   1.5025   NaN\n",
      "10  6560.29      1.5  0.843691  1.48433   NaN\n",
      "11  6828.66      1.5      0.99   1.4424   NaN\n",
      "==========init params=========\n",
      "m0 =   1.5834\n",
      "b =  10.8900\n",
      "gamma_k =   0.8437\n",
      "sigma =   0.4619\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.5863\n",
      "b =   8.7179\n",
      "gamma_k =   0.8692\n",
      "sigma =   0.4641\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   5875.94  6.31196  0.929625  1.53569   NaN\n",
      "1   5877.75  6.31196      0.99  1.53035   NaN\n",
      "2   5878.54  6.31196   0.86925  1.54013   NaN\n",
      "3   5880.01  8.71794      0.99  1.53818   NaN\n",
      "4   5886.38  8.71794   0.86925  1.58818   NaN\n",
      "5   5886.63  8.71794  0.929625  1.56091   NaN\n",
      "6   5894.55  3.90598   0.86925  1.52494   NaN\n",
      "7   5904.16  3.90598  0.929625  1.52328   NaN\n",
      "8   5935.58  3.90598      0.99  1.51845   NaN\n",
      "9   6484.99      1.5   0.86925  1.45035   NaN\n",
      "10  6573.27      1.5  0.929625  1.43927   NaN\n",
      "11  6740.68      1.5      0.99  1.41508   NaN\n",
      "==========init params=========\n",
      "m0 =   1.5357\n",
      "b =   6.3120\n",
      "gamma_k =   0.9296\n",
      "sigma =   0.4641\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.5341\n",
      "b =   6.2966\n",
      "gamma_k =   0.9565\n",
      "sigma =   0.4670\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0    5872.6  6.29655   0.95645   1.5453   NaN\n",
      "1    5873.7  6.29655  0.973225  1.54077   NaN\n",
      "2   5873.93   4.6977  0.973225  1.50085   NaN\n",
      "3   5874.05   4.6977   0.95645  1.50538   NaN\n",
      "4   5874.18   4.6977      0.99  1.49586   NaN\n",
      "5   5875.22  6.29655      0.99  1.52884   NaN\n",
      "6   5906.01  3.09885   0.95645  1.48246   NaN\n",
      "7   5913.38  3.09885  0.973225  1.48125   NaN\n",
      "8   5928.41  3.09885      0.99  1.47914   NaN\n",
      "9   6519.65      1.5   0.95645  1.41201   NaN\n",
      "10   6566.2      1.5  0.973225  1.40625   NaN\n",
      "11  6640.78      1.5      0.99  1.39638   NaN\n",
      "==========init params=========\n",
      "m0 =   1.5453\n",
      "b =   6.2966\n",
      "gamma_k =   0.9565\n",
      "sigma =   0.4670\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.5276\n",
      "b =   6.0069\n",
      "gamma_k =   0.9661\n",
      "sigma =   0.3914\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   5869.21  4.50457      0.99  1.48696   NaN\n",
      "1   5869.62  4.50457  0.978044  1.48992   NaN\n",
      "2   5870.31  4.50457  0.966087  1.49193   NaN\n",
      "3   5875.54  6.00685  0.966087  1.53599   NaN\n",
      "4   5876.12  6.00685      0.99  1.50863   NaN\n",
      "5   5876.24  6.00685  0.978044  1.52641   NaN\n",
      "6   5895.72  3.00228  0.966087  1.46034   NaN\n",
      "7   5900.77  3.00228  0.978044  1.45913   NaN\n",
      "8   5910.31  3.00228      0.99  1.45769   NaN\n",
      "9   6728.08      1.5  0.966087   1.4104   NaN\n",
      "10   6788.9      1.5  0.978044  1.40619   NaN\n",
      "11  6883.47      1.5      0.99  1.39922   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4870\n",
      "b =   4.5046\n",
      "gamma_k =   0.9900\n",
      "sigma =   0.3914\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.5128\n",
      "b =   5.6497\n",
      "gamma_k =   0.9748\n",
      "sigma =   0.5139\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   5863.71  4.26644      0.99  1.47697   NaN\n",
      "1   5864.37  4.26644  0.982399  1.47919   NaN\n",
      "2   5865.08  4.26644  0.974797  1.48071   NaN\n",
      "3   5872.13  2.88322  0.974797  1.44084   NaN\n",
      "4   5872.17  5.64965  0.974797  1.52514   NaN\n",
      "5   5872.21  5.64965      0.99   1.5083   NaN\n",
      "6   5872.34  5.64965  0.982399  1.51991   NaN\n",
      "7   5873.37  2.88322  0.982399  1.43947   NaN\n",
      "8   5875.42  2.88322      0.99  1.43765   NaN\n",
      "9   6289.57      1.5  0.974797  1.37885   NaN\n",
      "10  6313.21      1.5  0.982399  1.37624   NaN\n",
      "11   6346.9      1.5      0.99  1.37234   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4770\n",
      "b =   4.2664\n",
      "gamma_k =   0.9900\n",
      "sigma =   0.5139\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.4752\n",
      "b =   4.4308\n",
      "gamma_k =   0.9954\n",
      "sigma =   0.4863\n",
      "\n",
      "\n",
      "         LL        b        g        m sigma\n",
      "0   5863.16   3.4539  0.99542  1.44254   NaN\n",
      "1   5863.19   3.4539  0.99271  1.44505   NaN\n",
      "2   5863.29   3.4539     0.99  1.44674   NaN\n",
      "3      5867  4.43084  0.99542  1.47488   NaN\n",
      "4   5867.48  4.43084  0.99271  1.47817   NaN\n",
      "5   5867.85  4.43084     0.99  1.48054   NaN\n",
      "6   5876.67  2.47695     0.99  1.41046   NaN\n",
      "7   5877.99  2.47695  0.99271  1.40968   NaN\n",
      "8   5880.01  2.47695  0.99542  1.40868   NaN\n",
      "9   6307.63      1.5     0.99  1.36159   NaN\n",
      "10  6326.15      1.5  0.99271  1.35984   NaN\n",
      "11  6351.67      1.5  0.99542  1.35736   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4425\n",
      "b =   3.4539\n",
      "gamma_k =   0.9954\n",
      "sigma =   0.4863\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.4481\n",
      "b =   3.7617\n",
      "gamma_k =   0.9976\n",
      "sigma =   0.4610\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>m0</th>\n",
       "      <th>b</th>\n",
       "      <th>gamma_k</th>\n",
       "      <th>sigma</th>\n",
       "      <th>LL</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.796889</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>0.198939</td>\n",
       "      <td>0.629831</td>\n",
       "      <td>6451.792036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.776111</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>0.326086</td>\n",
       "      <td>0.542971</td>\n",
       "      <td>6106.053752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.693020</td>\n",
       "      <td>12.457074</td>\n",
       "      <td>0.311943</td>\n",
       "      <td>0.565602</td>\n",
       "      <td>5959.710137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.654031</td>\n",
       "      <td>15.584963</td>\n",
       "      <td>0.697383</td>\n",
       "      <td>0.461888</td>\n",
       "      <td>5900.663844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.586325</td>\n",
       "      <td>8.717936</td>\n",
       "      <td>0.869250</td>\n",
       "      <td>0.464081</td>\n",
       "      <td>5883.238714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.534078</td>\n",
       "      <td>6.296554</td>\n",
       "      <td>0.956450</td>\n",
       "      <td>0.466958</td>\n",
       "      <td>5875.473759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.527624</td>\n",
       "      <td>6.006854</td>\n",
       "      <td>0.966087</td>\n",
       "      <td>0.391437</td>\n",
       "      <td>5870.013921</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.512750</td>\n",
       "      <td>5.649653</td>\n",
       "      <td>0.974797</td>\n",
       "      <td>0.513890</td>\n",
       "      <td>5863.189012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.475161</td>\n",
       "      <td>4.430843</td>\n",
       "      <td>0.995420</td>\n",
       "      <td>0.486330</td>\n",
       "      <td>5862.997348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.448112</td>\n",
       "      <td>3.761698</td>\n",
       "      <td>0.997645</td>\n",
       "      <td>0.461049</td>\n",
       "      <td>5862.674907</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         m0          b   gamma_k     sigma           LL\n",
       "0  1.796889   1.500000  0.198939  0.629831  6451.792036\n",
       "1  1.776111  50.000000  0.326086  0.542971  6106.053752\n",
       "2  1.693020  12.457074  0.311943  0.565602  5959.710137\n",
       "3  1.654031  15.584963  0.697383  0.461888  5900.663844\n",
       "4  1.586325   8.717936  0.869250  0.464081  5883.238714\n",
       "5  1.534078   6.296554  0.956450  0.466958  5875.473759\n",
       "6  1.527624   6.006854  0.966087  0.391437  5870.013921\n",
       "7  1.512750   5.649653  0.974797  0.513890  5863.189012\n",
       "8  1.475161   4.430843  0.995420  0.486330  5862.997348\n",
       "9  1.448112   3.761698  0.997645  0.461049  5862.674907"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "op_methods = 'slsqp'\n",
    "row = 1\n",
    "dum_data = raw[row]\n",
    "returns = np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "a = returns.to_frame()\n",
    "data = a['Column2']*100\n",
    "data2 = data#[::-1]\n",
    "startingvals = []\n",
    "\n",
    "for i in range(0,10):\n",
    "    kbar = i+1\n",
    "    if kbar >1 and bool(result):\n",
    "        startingvals = [result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value]\n",
    "    result = MSM_fitdata(data, kbar, LB ,UB,op_methods, startingvals)\n",
    "    re2 = MSM_likelihood_new(result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value,  kbar, data2)\n",
    "    output.loc[i,\"LL\"] = re2\n",
    "    for element in result.params:\n",
    "        output.loc[i,element] = result.params[element].value\n",
    "        \n",
    "writer = pd.ExcelWriter('Output'.join((date.today().strftime('%y%m%d'),op_methods+'JPYvaryk.xlsx')))\n",
    "output.to_excel(writer, 'Sheet1')\n",
    "writer.save()\n",
    "        \n",
    "output  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### GBP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-18T13:45:23.946378Z",
     "start_time": "2018-02-18T13:45:23.941367Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kbar >1 and bool([])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-18T15:22:45.644133Z",
     "start_time": "2018-02-18T14:58:34.722237Z"
    },
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "         LL    b     g        m sigma\n",
      "0   5960.39  1.5   0.1  1.71092   NaN\n",
      "1   5960.39    3   0.1  1.71092   NaN\n",
      "2   5960.39    6   0.1  1.71092   NaN\n",
      "3   5960.39   20   0.1  1.71092   NaN\n",
      "4   6042.08  1.5   0.5  1.79291   NaN\n",
      "5   6042.08    3   0.5  1.79291   NaN\n",
      "6   6042.08    6   0.5  1.79291   NaN\n",
      "7   6042.08   20   0.5  1.79291   NaN\n",
      "8   6195.76  1.5  0.99  1.78486   NaN\n",
      "9   6195.76    3  0.99  1.78486   NaN\n",
      "10  6195.76    6  0.99  1.78486   NaN\n",
      "11  6195.76   20  0.99  1.78486   NaN\n",
      "==========init params=========\n",
      "m0 =   1.7109\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.6069\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.7157\n",
      "b =   1.5000\n",
      "gamma_k =   0.1099\n",
      "sigma =   0.6087\n",
      "\n",
      "\n",
      "2\n",
      "         LL    b         g        m sigma\n",
      "0   5766.16  1.5  0.109946  1.65469   NaN\n",
      "1   5766.16  1.5  0.109946  1.65469   NaN\n",
      "2   5766.16  1.5  0.109946  1.65469   NaN\n",
      "3   5766.16  1.5  0.109946  1.65469   NaN\n",
      "4   5938.49  1.5  0.549973  1.67616   NaN\n",
      "5   5938.49  1.5  0.549973  1.67616   NaN\n",
      "6   5938.49  1.5  0.549973  1.67616   NaN\n",
      "7   5938.49  1.5  0.549973  1.67616   NaN\n",
      "8   6134.94  1.5      0.99  1.64867   NaN\n",
      "9   6134.94  1.5      0.99  1.64867   NaN\n",
      "10  6134.94  1.5      0.99  1.64867   NaN\n",
      "11  6134.94  1.5      0.99  1.64867   NaN\n",
      "==========init params=========\n",
      "m0 =   1.6547\n",
      "b =   1.5000\n",
      "gamma_k =   0.1099\n",
      "sigma =   0.6087\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.6715\n",
      "b =  19.9051\n",
      "gamma_k =   0.2222\n",
      "sigma =   0.5895\n",
      "\n",
      "\n",
      "3\n",
      "         LL        b         g        m sigma\n",
      "0   5630.78  13.7701  0.222162  1.66541   NaN\n",
      "1   5633.36  19.9051  0.222162  1.66549   NaN\n",
      "2   5636.12  7.63504  0.222162  1.65588   NaN\n",
      "3    5638.8  19.9051  0.606081   1.6524   NaN\n",
      "4   5639.54  13.7701  0.606081  1.63683   NaN\n",
      "5   5656.63  7.63504  0.606081  1.61859   NaN\n",
      "6    5677.7  19.9051      0.99  1.61706   NaN\n",
      "7   5702.61  13.7701      0.99  1.60989   NaN\n",
      "8   5737.05      1.5  0.222162  1.58817   NaN\n",
      "9   5775.23  7.63504      0.99  1.59757   NaN\n",
      "10  5902.99      1.5  0.606081  1.58337   NaN\n",
      "11  6114.47      1.5      0.99  1.54873   NaN\n",
      "==========init params=========\n",
      "m0 =   1.6654\n",
      "b =  13.7701\n",
      "gamma_k =   0.2222\n",
      "sigma =   0.5895\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.6477\n",
      "b =  14.2864\n",
      "gamma_k =   0.2780\n",
      "sigma =   0.5134\n",
      "\n",
      "\n",
      "4\n",
      "         LL        b         g        m sigma\n",
      "0   5571.69  14.2864  0.633994  1.61285   NaN\n",
      "1   5574.49  10.0242  0.633994  1.60209   NaN\n",
      "2    5577.3  10.0242  0.277987  1.62001   NaN\n",
      "3   5578.67  14.2864  0.277987  1.62785   NaN\n",
      "4   5583.52  5.76212  0.277987  1.60019   NaN\n",
      "5   5601.04  5.76212  0.633994  1.58413   NaN\n",
      "6   5607.99  14.2864      0.99  1.59254   NaN\n",
      "7   5628.64  10.0242      0.99  1.57317   NaN\n",
      "8   5695.81  5.76212      0.99  1.53893   NaN\n",
      "9   5738.93      1.5  0.277987  1.51839   NaN\n",
      "10  5914.06      1.5  0.633994  1.49909   NaN\n",
      "11  6174.57      1.5      0.99  1.45411   NaN\n",
      "==========init params=========\n",
      "m0 =   1.6129\n",
      "b =  14.2864\n",
      "gamma_k =   0.6340\n",
      "sigma =   0.5134\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.6092\n",
      "b =  12.5064\n",
      "gamma_k =   0.6449\n",
      "sigma =   0.4672\n",
      "\n",
      "\n",
      "5\n",
      "         LL        b        g        m sigma\n",
      "0   5540.09  12.5064  0.64494  1.58371   NaN\n",
      "1   5544.82  8.83763  0.64494  1.57566   NaN\n",
      "2   5546.65  12.5064  0.81747  1.57782   NaN\n",
      "3   5554.31  8.83763  0.81747  1.56025   NaN\n",
      "4   5566.59  5.16881  0.64494  1.54307   NaN\n",
      "5   5569.52  12.5064     0.99  1.55122   NaN\n",
      "6   5577.99  8.83763     0.99  1.53523   NaN\n",
      "7   5579.71  5.16881  0.81747  1.52819   NaN\n",
      "8   5628.19  5.16881     0.99  1.51391   NaN\n",
      "9    5928.7      1.5  0.64494  1.45492   NaN\n",
      "10  6047.57      1.5  0.81747  1.44275   NaN\n",
      "11  6266.79      1.5     0.99  1.40913   NaN\n",
      "==========init params=========\n",
      "m0 =   1.5837\n",
      "b =  12.5064\n",
      "gamma_k =   0.6449\n",
      "sigma =   0.4672\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.5789\n",
      "b =  11.0175\n",
      "gamma_k =   0.6371\n",
      "sigma =   0.4213\n",
      "\n",
      "\n",
      "6\n",
      "         LL        b         g        m sigma\n",
      "0   5527.13  7.84502  0.637128  1.53234   NaN\n",
      "1   5527.81  7.84502  0.813564  1.52511   NaN\n",
      "2   5528.04  11.0175  0.813564  1.53878   NaN\n",
      "3   5530.85  11.0175  0.637128  1.54535   NaN\n",
      "4   5535.15  11.0175      0.99   1.5227   NaN\n",
      "5   5537.59  4.67251  0.637128  1.50893   NaN\n",
      "6   5540.36  7.84502      0.99  1.51501   NaN\n",
      "7   5545.94  4.67251  0.813564  1.50567   NaN\n",
      "8   5587.49  4.67251      0.99  1.49075   NaN\n",
      "9   5948.32      1.5  0.637128  1.43288   NaN\n",
      "10  6098.58      1.5  0.813564  1.42169   NaN\n",
      "11  6414.45      1.5      0.99  1.38807   NaN\n",
      "==========init params=========\n",
      "m0 =   1.5323\n",
      "b =   7.8450\n",
      "gamma_k =   0.6371\n",
      "sigma =   0.4213\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.5337\n",
      "b =   8.3156\n",
      "gamma_k =   0.7835\n",
      "sigma =   0.4676\n",
      "\n",
      "\n",
      "7\n",
      "         LL        b         g        m sigma\n",
      "0   5524.03  6.04375  0.886737  1.49789   NaN\n",
      "1   5524.54  6.04375  0.783474  1.50532   NaN\n",
      "2   5527.18  6.04375      0.99  1.48397   NaN\n",
      "3   5527.55  8.31563      0.99  1.50077   NaN\n",
      "4    5528.7  8.31563  0.783474  1.53149   NaN\n",
      "5   5528.84  8.31563  0.886737   1.5185   NaN\n",
      "6   5534.69  3.77188  0.783474  1.47308   NaN\n",
      "7   5540.67  3.77188  0.886737  1.46664   NaN\n",
      "8   5563.69  3.77188      0.99  1.45256   NaN\n",
      "9   5881.31      1.5  0.783474  1.39092   NaN\n",
      "10  5962.68      1.5  0.886737  1.38435   NaN\n",
      "11  6143.87      1.5      0.99  1.36424   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4979\n",
      "b =   6.0438\n",
      "gamma_k =   0.8867\n",
      "sigma =   0.4676\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.5033\n",
      "b =   6.7155\n",
      "gamma_k =   0.8113\n",
      "sigma =   0.3891\n",
      "\n",
      "\n",
      "8\n",
      "         LL        b         g        m sigma\n",
      "0   5515.99  4.97698  0.900661  1.46103   NaN\n",
      "1   5518.03  6.71548      0.99  1.46649   NaN\n",
      "2    5518.1  4.97698      0.99  1.45477   NaN\n",
      "3    5518.6  4.97698  0.811321  1.46415   NaN\n",
      "4   5525.19  6.71548  0.900661  1.47856   NaN\n",
      "5   5527.66  6.71548  0.811321  1.50637   NaN\n",
      "6   5528.64  3.23849  0.811321  1.44138   NaN\n",
      "7   5535.31  3.23849  0.900661  1.43889   NaN\n",
      "8   5561.11  3.23849      0.99  1.43262   NaN\n",
      "9    6004.8      1.5  0.811321   1.3883   NaN\n",
      "10   6119.3      1.5  0.900661  1.38237   NaN\n",
      "11  6392.52      1.5      0.99  1.36384   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4610\n",
      "b =   4.9770\n",
      "gamma_k =   0.9007\n",
      "sigma =   0.3891\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.4605\n",
      "b =   5.2325\n",
      "gamma_k =   0.9584\n",
      "sigma =   0.3838\n",
      "\n",
      "\n",
      "9\n",
      "         LL        b         g        m sigma\n",
      "0   5515.38  3.98835  0.958404  1.42731   NaN\n",
      "1   5515.52  3.98835  0.974202  1.42603   NaN\n",
      "2   5516.62  3.98835      0.99  1.42426   NaN\n",
      "3   5519.72  5.23253      0.99  1.43764   NaN\n",
      "4   5521.11  5.23253  0.974202  1.44299   NaN\n",
      "5   5522.06  5.23253  0.958404  1.45096   NaN\n",
      "6    5544.2  2.74418  0.958404  1.40838   NaN\n",
      "7   5549.79  2.74418  0.974202  1.40748   NaN\n",
      "8   5560.64  2.74418      0.99  1.40594   NaN\n",
      "9   6145.63      1.5  0.958404  1.36244   NaN\n",
      "10  6200.84      1.5  0.974202  1.35936   NaN\n",
      "11  6294.85      1.5      0.99  1.35362   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4273\n",
      "b =   3.9884\n",
      "gamma_k =   0.9584\n",
      "sigma =   0.3838\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.4282\n",
      "b =   4.0752\n",
      "gamma_k =   0.9644\n",
      "sigma =   0.3736\n",
      "\n",
      "\n",
      "10\n",
      "         LL        b         g        m sigma\n",
      "0   5515.31  3.21683  0.964411  1.40086   NaN\n",
      "1   5515.67  3.21683  0.977206  1.39973   NaN\n",
      "2   5516.99  3.21683      0.99   1.3981   NaN\n",
      "3   5517.95  4.07524      0.99    1.413   NaN\n",
      "4   5518.76  4.07524  0.977206  1.41918   NaN\n",
      "5   5519.07  4.07524  0.964411  1.42728   NaN\n",
      "6   5554.17  2.35841  0.964411  1.38352   NaN\n",
      "7   5560.51  2.35841  0.977206  1.38298   NaN\n",
      "8   5572.05  2.35841      0.99  1.38218   NaN\n",
      "9   6084.47      1.5  0.964411  1.35257   NaN\n",
      "10  6133.24      1.5  0.977206  1.35044   NaN\n",
      "11  6213.88      1.5      0.99  1.34657   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4009\n",
      "b =   3.2168\n",
      "gamma_k =   0.9644\n",
      "sigma =   0.3736\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.4030\n",
      "b =   3.4507\n",
      "gamma_k =   0.9818\n",
      "sigma =   0.3704\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>m0</th>\n",
       "      <th>b</th>\n",
       "      <th>gamma_k</th>\n",
       "      <th>sigma</th>\n",
       "      <th>LL</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.715749</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>0.109946</td>\n",
       "      <td>0.608671</td>\n",
       "      <td>5960.169424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.671453</td>\n",
       "      <td>19.905125</td>\n",
       "      <td>0.222162</td>\n",
       "      <td>0.589502</td>\n",
       "      <td>5724.358738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.647739</td>\n",
       "      <td>14.286373</td>\n",
       "      <td>0.277987</td>\n",
       "      <td>0.513368</td>\n",
       "      <td>5622.725978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.609153</td>\n",
       "      <td>12.506440</td>\n",
       "      <td>0.644940</td>\n",
       "      <td>0.467186</td>\n",
       "      <td>5570.014433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.578921</td>\n",
       "      <td>11.017527</td>\n",
       "      <td>0.637128</td>\n",
       "      <td>0.421256</td>\n",
       "      <td>5537.792457</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.533702</td>\n",
       "      <td>8.315625</td>\n",
       "      <td>0.783474</td>\n",
       "      <td>0.467635</td>\n",
       "      <td>5523.628778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.503309</td>\n",
       "      <td>6.715476</td>\n",
       "      <td>0.811321</td>\n",
       "      <td>0.389147</td>\n",
       "      <td>5516.877211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.460527</td>\n",
       "      <td>5.232527</td>\n",
       "      <td>0.958404</td>\n",
       "      <td>0.383777</td>\n",
       "      <td>5515.366208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.428160</td>\n",
       "      <td>4.075240</td>\n",
       "      <td>0.964411</td>\n",
       "      <td>0.373594</td>\n",
       "      <td>5515.268775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.402960</td>\n",
       "      <td>3.450710</td>\n",
       "      <td>0.981753</td>\n",
       "      <td>0.370389</td>\n",
       "      <td>5514.933868</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         m0          b   gamma_k     sigma           LL\n",
       "0  1.715749   1.500000  0.109946  0.608671  5960.169424\n",
       "1  1.671453  19.905125  0.222162  0.589502  5724.358738\n",
       "2  1.647739  14.286373  0.277987  0.513368  5622.725978\n",
       "3  1.609153  12.506440  0.644940  0.467186  5570.014433\n",
       "4  1.578921  11.017527  0.637128  0.421256  5537.792457\n",
       "5  1.533702   8.315625  0.783474  0.467635  5523.628778\n",
       "6  1.503309   6.715476  0.811321  0.389147  5516.877211\n",
       "7  1.460527   5.232527  0.958404  0.383777  5515.366208\n",
       "8  1.428160   4.075240  0.964411  0.373594  5515.268775\n",
       "9  1.402960   3.450710  0.981753  0.370389  5514.933868"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "op_methods = 'slsqp'\n",
    "row = 2\n",
    "dum_data = raw[row]\n",
    "returns = np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "a = returns.to_frame()\n",
    "data = a['Column2']*100\n",
    "data2 = data#[::-1]\n",
    "startingvals = []\n",
    "\n",
    "\n",
    "for i in range(0,10):\n",
    "    kbar = i+1\n",
    "    print(kbar)\n",
    "    \n",
    "    if kbar >1 and bool(result):\n",
    "        startingvals = [result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value]\n",
    "    \n",
    "    result = MSM_fitdata(data, kbar, LB ,UB,op_methods, startingvals)\n",
    "    re2 = MSM_likelihood_new(result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value,  kbar, data2)\n",
    "    output.loc[i,\"LL\"] = re2\n",
    "    for element in result.params:\n",
    "        output.loc[i,element] = result.params[element].value\n",
    "        \n",
    "writer = pd.ExcelWriter('Output'.join((date.today().strftime('%y%m%d'),op_methods+'GBPvaryk5.xlsx')))\n",
    "output.to_excel(writer, 'Sheet1')\n",
    "writer.save()\n",
    "        \n",
    "output  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CAD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-18T16:04:20.143676Z",
     "start_time": "2018-02-18T15:24:46.992167Z"
    },
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         LL    b     g        m sigma\n",
      "0   277.435  1.5   0.1  1.66057   NaN\n",
      "1   277.435    3   0.1  1.66057   NaN\n",
      "2   277.435    6   0.1  1.66057   NaN\n",
      "3   277.435   20   0.1  1.66057   NaN\n",
      "4   422.325  1.5   0.5  1.71418   NaN\n",
      "5   422.325    3   0.5  1.71418   NaN\n",
      "6   422.325    6   0.5  1.71418   NaN\n",
      "7   422.325   20   0.5  1.71418   NaN\n",
      "8   550.776  1.5  0.99  1.69648   NaN\n",
      "9   550.776    3  0.99  1.69648   NaN\n",
      "10  550.776    6  0.99  1.69648   NaN\n",
      "11  550.776   20  0.99  1.69648   NaN\n",
      "==========init params=========\n",
      "m0 =   1.6606\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.2744\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = lbgfsb\n",
      "m0 =   1.6459\n",
      "b =   1.8901\n",
      "gamma_k =   0.0638\n",
      "sigma =   0.2799\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   143.498  1.89008  0.063751  1.54284   NaN\n",
      "1   144.306  1.76005  0.063751  1.54288   NaN\n",
      "2   145.193  1.63003  0.063751  1.54297   NaN\n",
      "3   146.169      1.5  0.063751  1.54314   NaN\n",
      "4   331.158  1.89008  0.526876  1.58396   NaN\n",
      "5   337.083  1.76005  0.526876  1.58416   NaN\n",
      "6    343.29  1.63003  0.526876  1.58436   NaN\n",
      "7    349.79      1.5  0.526876  1.58458   NaN\n",
      "8   500.926  1.89008      0.99  1.56998   NaN\n",
      "9    502.95  1.76005      0.99  1.56936   NaN\n",
      "10  504.861  1.63003      0.99  1.56877   NaN\n",
      "11  506.631      1.5      0.99  1.56821   NaN\n",
      "==========init params=========\n",
      "m0 =   1.5428\n",
      "b =   1.8901\n",
      "gamma_k =   0.0638\n",
      "sigma =   0.2799\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = lbgfsb\n",
      "m0 =   1.5560\n",
      "b =  10.9241\n",
      "gamma_k =   0.1094\n",
      "sigma =   0.2775\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   106.914  4.64137  0.109383  1.46571   NaN\n",
      "1   111.617  10.9241  0.549691  1.49322   NaN\n",
      "2   112.836  7.78275  0.109383  1.47187   NaN\n",
      "3   119.069  7.78275  0.549691  1.49232   NaN\n",
      "4   119.893  10.9241  0.109383  1.47927   NaN\n",
      "5   132.454      1.5  0.109383  1.45905   NaN\n",
      "6   149.674  4.64137  0.549691   1.4888   NaN\n",
      "7   184.343  10.9241      0.99  1.50028   NaN\n",
      "8   223.082  7.78275      0.99  1.50092   NaN\n",
      "9   312.205  4.64137      0.99  1.50186   NaN\n",
      "10  313.986      1.5  0.549691  1.49426   NaN\n",
      "11  486.524      1.5      0.99  1.48151   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4657\n",
      "b =   4.6414\n",
      "gamma_k =   0.1094\n",
      "sigma =   0.2775\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = lbgfsb\n",
      "m0 =   1.4739\n",
      "b =   4.7589\n",
      "gamma_k =   0.1290\n",
      "sigma =   0.2929\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   95.1454  3.67258  0.128981  1.45376   NaN\n",
      "1   96.3879  4.75888  0.128981  1.46536   NaN\n",
      "2   97.9673  2.58629  0.128981   1.4312   NaN\n",
      "3   105.586  4.75888  0.559491  1.43625   NaN\n",
      "4   121.281  3.67258  0.559491  1.43513   NaN\n",
      "5   124.789      1.5  0.128981  1.41798   NaN\n",
      "6   164.405  2.58629  0.559491  1.43723   NaN\n",
      "7   191.185  4.75888      0.99  1.45168   NaN\n",
      "8   248.042  3.67258      0.99  1.45548   NaN\n",
      "9    288.68      1.5  0.559491  1.45016   NaN\n",
      "10  349.779  2.58629      0.99  1.45993   NaN\n",
      "11  480.554      1.5      0.99  1.45195   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4538\n",
      "b =   3.6726\n",
      "gamma_k =   0.1290\n",
      "sigma =   0.2929\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = lbgfsb\n",
      "m0 =   1.4351\n",
      "b =   3.9485\n",
      "gamma_k =   0.1707\n",
      "sigma =   0.2635\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   90.6194  3.94846  0.580354  1.38383   NaN\n",
      "1   92.2368  3.13231  0.170709  1.38819   NaN\n",
      "2   92.3527  2.31615  0.170709  1.37106   NaN\n",
      "3   95.6532  3.94846  0.170709  1.41211   NaN\n",
      "4   98.9204  3.13231  0.580354  1.37589   NaN\n",
      "5   120.494      1.5  0.170709  1.35922   NaN\n",
      "6    133.33  2.31615  0.580354  1.37357   NaN\n",
      "7   138.874  3.94846      0.99  1.38604   NaN\n",
      "8   187.839  3.13231      0.99  1.38738   NaN\n",
      "9   251.551      1.5  0.580354  1.37972   NaN\n",
      "10  292.545  2.31615      0.99   1.3878   NaN\n",
      "11  448.794      1.5      0.99  1.37253   NaN\n",
      "==========init params=========\n",
      "m0 =   1.3838\n",
      "b =   3.9485\n",
      "gamma_k =   0.5804\n",
      "sigma =   0.2635\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = lbgfsb\n",
      "m0 =   1.3865\n",
      "b =   4.0226\n",
      "gamma_k =   0.4414\n",
      "sigma =   0.2510\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   87.7709  3.18173  0.441384  1.35244   NaN\n",
      "1     89.61  4.02259  0.715692  1.35833   NaN\n",
      "2   89.8965  4.02259  0.441384  1.37692   NaN\n",
      "3   90.2635  3.18173  0.715692  1.34686   NaN\n",
      "4   94.6983  2.34086  0.441384  1.33659   NaN\n",
      "5   101.743  4.02259      0.99  1.35108   NaN\n",
      "6   118.366  2.34086  0.715692  1.33971   NaN\n",
      "7   127.692  3.18173      0.99  1.34778   NaN\n",
      "8   182.164      1.5  0.441384  1.33459   NaN\n",
      "9   218.076  2.34086      0.99  1.34893   NaN\n",
      "10  269.549      1.5  0.715692  1.34311   NaN\n",
      "11  437.121      1.5      0.99  1.33454   NaN\n",
      "==========init params=========\n",
      "m0 =   1.3524\n",
      "b =   3.1817\n",
      "gamma_k =   0.4414\n",
      "sigma =   0.2510\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = lbgfsb\n",
      "m0 =   1.3738\n",
      "b =   4.0758\n",
      "gamma_k =   0.5239\n",
      "sigma =   0.2947\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   85.2493  3.21717  0.523879  1.34459   NaN\n",
      "1   85.8995  3.21717  0.756939  1.33956   NaN\n",
      "2    87.605  4.07576  0.756939  1.35539   NaN\n",
      "3   89.3834  4.07576  0.523879  1.37385   NaN\n",
      "4   91.1194  2.35859  0.523879  1.32858   NaN\n",
      "5    92.927  4.07576      0.99  1.34219   NaN\n",
      "6   105.332  2.35859  0.756939  1.33119   NaN\n",
      "7     107.1  3.21717      0.99  1.33744   NaN\n",
      "8   164.215  2.35859      0.99  1.34395   NaN\n",
      "9   182.376      1.5  0.523879  1.33632   NaN\n",
      "10  250.512      1.5  0.756939  1.34949   NaN\n",
      "11  399.128      1.5      0.99  1.35984   NaN\n",
      "==========init params=========\n",
      "m0 =   1.3446\n",
      "b =   3.2172\n",
      "gamma_k =   0.5239\n",
      "sigma =   0.2947\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = lbgfsb\n",
      "m0 =   1.3376\n",
      "b =   3.1110\n",
      "gamma_k =   0.5933\n",
      "sigma =   0.2819\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   83.8535  2.57403  0.593339  1.31348   NaN\n",
      "1   85.3669  3.11104  0.791669  1.32381   NaN\n",
      "2   86.1021  3.11104  0.593339  1.33508   NaN\n",
      "3   86.1836  2.57403  0.791669  1.30929   NaN\n",
      "4   92.3441  3.11104      0.99  1.31297   NaN\n",
      "5   92.5538  2.03701  0.593339  1.30122   NaN\n",
      "6   106.883  2.03701  0.791669  1.30412   NaN\n",
      "7    107.19  2.57403      0.99   1.3095   NaN\n",
      "8   165.652  2.03701      0.99  1.31518   NaN\n",
      "9   166.033      1.5  0.593339  1.30687   NaN\n",
      "10  219.419      1.5  0.791669  1.31633   NaN\n",
      "11  351.663      1.5      0.99  1.32517   NaN\n",
      "==========init params=========\n",
      "m0 =   1.3135\n",
      "b =   2.5740\n",
      "gamma_k =   0.5933\n",
      "sigma =   0.2819\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = lbgfsb\n",
      "m0 =   1.3192\n",
      "b =   2.7233\n",
      "gamma_k =   0.5950\n",
      "sigma =   0.2624\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   83.0951  2.31555  0.594994  1.29573   NaN\n",
      "1   84.1791  2.72333  0.792497  1.30469   NaN\n",
      "2   84.6198  2.31555  0.792497  1.28827   NaN\n",
      "3   85.4583  2.72333  0.594994  1.31541   NaN\n",
      "4   88.2352  1.90778  0.594994  1.27847   NaN\n",
      "5   90.1565  2.72333      0.99  1.29044   NaN\n",
      "6   98.8541  1.90778  0.792497  1.27921   NaN\n",
      "7   100.557  2.31555      0.99  1.28459   NaN\n",
      "8   139.933      1.5  0.594994  1.27734   NaN\n",
      "9   150.239  1.90778      0.99  1.28663   NaN\n",
      "10   184.71      1.5  0.792497  1.28452   NaN\n",
      "11  311.025      1.5      0.99  1.29171   NaN\n",
      "==========init params=========\n",
      "m0 =   1.2957\n",
      "b =   2.3156\n",
      "gamma_k =   0.5950\n",
      "sigma =   0.2624\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = lbgfsb\n",
      "m0 =   1.2958\n",
      "b =   2.3507\n",
      "gamma_k =   0.6309\n",
      "sigma =   0.2594\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   83.0339   2.0671  0.630917  1.27587   NaN\n",
      "1   83.7779  2.35065  0.810458  1.28316   NaN\n",
      "2   84.2335  2.35065  0.630917  1.29247   NaN\n",
      "3   85.0632   2.0671  0.810458  1.27053   NaN\n",
      "4   88.6875  1.78355  0.630917  1.26305   NaN\n",
      "5   90.4527  2.35065      0.99  1.27252   NaN\n",
      "6   99.0758  1.78355  0.810458  1.26376   NaN\n",
      "7   102.568   2.0671      0.99   1.2683   NaN\n",
      "8   126.915      1.5  0.630917  1.26146   NaN\n",
      "9   148.104  1.78355      0.99  1.27044   NaN\n",
      "10  162.342      1.5  0.810458  1.26726   NaN\n",
      "11  272.036      1.5      0.99   1.2755   NaN\n",
      "==========init params=========\n",
      "m0 =   1.2759\n",
      "b =   2.0671\n",
      "gamma_k =   0.6309\n",
      "sigma =   0.2594\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = lbgfsb\n",
      "m0 =   1.2777\n",
      "b =   2.1084\n",
      "gamma_k =   0.6439\n",
      "sigma =   0.2616\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>m0</th>\n",
       "      <th>b</th>\n",
       "      <th>gamma_k</th>\n",
       "      <th>sigma</th>\n",
       "      <th>LL</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.645898</td>\n",
       "      <td>1.890077</td>\n",
       "      <td>0.063751</td>\n",
       "      <td>0.279945</td>\n",
       "      <td>271.002919</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.555995</td>\n",
       "      <td>10.924122</td>\n",
       "      <td>0.109383</td>\n",
       "      <td>0.277510</td>\n",
       "      <td>129.793835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.473888</td>\n",
       "      <td>4.758877</td>\n",
       "      <td>0.128981</td>\n",
       "      <td>0.292861</td>\n",
       "      <td>105.152252</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.435084</td>\n",
       "      <td>3.948461</td>\n",
       "      <td>0.170709</td>\n",
       "      <td>0.263496</td>\n",
       "      <td>91.314827</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.386468</td>\n",
       "      <td>4.022594</td>\n",
       "      <td>0.441384</td>\n",
       "      <td>0.251030</td>\n",
       "      <td>88.401337</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.373756</td>\n",
       "      <td>4.075756</td>\n",
       "      <td>0.523879</td>\n",
       "      <td>0.294691</td>\n",
       "      <td>84.719261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.337553</td>\n",
       "      <td>3.111044</td>\n",
       "      <td>0.593339</td>\n",
       "      <td>0.281890</td>\n",
       "      <td>84.022924</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.319242</td>\n",
       "      <td>2.723327</td>\n",
       "      <td>0.594994</td>\n",
       "      <td>0.262433</td>\n",
       "      <td>83.389001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.295804</td>\n",
       "      <td>2.350653</td>\n",
       "      <td>0.630917</td>\n",
       "      <td>0.259362</td>\n",
       "      <td>83.046985</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.277733</td>\n",
       "      <td>2.108387</td>\n",
       "      <td>0.643876</td>\n",
       "      <td>0.261617</td>\n",
       "      <td>82.989752</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         m0          b   gamma_k     sigma          LL\n",
       "0  1.645898   1.890077  0.063751  0.279945  271.002919\n",
       "1  1.555995  10.924122  0.109383  0.277510  129.793835\n",
       "2  1.473888   4.758877  0.128981  0.292861  105.152252\n",
       "3  1.435084   3.948461  0.170709  0.263496   91.314827\n",
       "4  1.386468   4.022594  0.441384  0.251030   88.401337\n",
       "5  1.373756   4.075756  0.523879  0.294691   84.719261\n",
       "6  1.337553   3.111044  0.593339  0.281890   84.022924\n",
       "7  1.319242   2.723327  0.594994  0.262433   83.389001\n",
       "8  1.295804   2.350653  0.630917  0.259362   83.046985\n",
       "9  1.277733   2.108387  0.643876  0.261617   82.989752"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "op_methods = 'slsqp'\n",
    "row = 3\n",
    "dum_data = raw[row]\n",
    "returns = np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "a = returns.to_frame()\n",
    "data = a['Column2']*100\n",
    "data2 = data#[::-1]\n",
    "startingvals = []\n",
    "\n",
    "for i in range(0,10):\n",
    "    kbar = i+1\n",
    "    if kbar >1 and bool(result):\n",
    "        startingvals = [result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value]\n",
    "    result = MSM_fitdata(data, kbar, LB ,UB,op_methods, startingvals)\n",
    "    re2 = MSM_likelihood_new(result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value,  kbar, data2)\n",
    "    output.loc[i,\"LL\"] = re2\n",
    "    for element in result.params:\n",
    "        output.loc[i,element] = result.params[element].value\n",
    "\n",
    "writer = pd.ExcelWriter('Output'.join((date.today().strftime('%y%m%d'),op_methods+'CADvaryk.xlsx')))\n",
    "output.to_excel(writer, 'Sheet1')\n",
    "writer.save()\n",
    "\n",
    "output  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## export set of params to .xlsx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-18T14:44:20.510291Z",
     "start_time": "2018-02-18T14:44:20.497708Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>m0</th>\n",
       "      <th>b</th>\n",
       "      <th>gamma_k</th>\n",
       "      <th>sigma</th>\n",
       "      <th>LL</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.724131</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>0.129090</td>\n",
       "      <td>0.608754</td>\n",
       "      <td>5967.526625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.673841</td>\n",
       "      <td>21.302960</td>\n",
       "      <td>0.245566</td>\n",
       "      <td>0.587575</td>\n",
       "      <td>5727.634096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.649398</td>\n",
       "      <td>15.651842</td>\n",
       "      <td>0.324070</td>\n",
       "      <td>0.508946</td>\n",
       "      <td>5625.049883</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.609224</td>\n",
       "      <td>12.765558</td>\n",
       "      <td>0.659629</td>\n",
       "      <td>0.467231</td>\n",
       "      <td>5570.547290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.579176</td>\n",
       "      <td>11.205719</td>\n",
       "      <td>0.650867</td>\n",
       "      <td>0.420608</td>\n",
       "      <td>5538.345034</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.533688</td>\n",
       "      <td>8.403110</td>\n",
       "      <td>0.792995</td>\n",
       "      <td>0.467599</td>\n",
       "      <td>5523.897339</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.585299</td>\n",
       "      <td>49.864345</td>\n",
       "      <td>0.956547</td>\n",
       "      <td>0.294231</td>\n",
       "      <td>5563.227019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.609050</td>\n",
       "      <td>44.049004</td>\n",
       "      <td>0.392482</td>\n",
       "      <td>0.471145</td>\n",
       "      <td>5586.177678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.460462</td>\n",
       "      <td>5.237711</td>\n",
       "      <td>0.959639</td>\n",
       "      <td>0.522382</td>\n",
       "      <td>5515.864436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.402961</td>\n",
       "      <td>3.450525</td>\n",
       "      <td>0.981728</td>\n",
       "      <td>0.370388</td>\n",
       "      <td>5514.933868</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         m0          b   gamma_k     sigma           LL\n",
       "0  1.724131   1.500000  0.129090  0.608754  5967.526625\n",
       "1  1.673841  21.302960  0.245566  0.587575  5727.634096\n",
       "2  1.649398  15.651842  0.324070  0.508946  5625.049883\n",
       "3  1.609224  12.765558  0.659629  0.467231  5570.547290\n",
       "4  1.579176  11.205719  0.650867  0.420608  5538.345034\n",
       "5  1.533688   8.403110  0.792995  0.467599  5523.897339\n",
       "6  1.585299  49.864345  0.956547  0.294231  5563.227019\n",
       "7  1.609050  44.049004  0.392482  0.471145  5586.177678\n",
       "8  1.460462   5.237711  0.959639  0.522382  5515.864436\n",
       "9  1.402961   3.450525  0.981728  0.370388  5514.933868"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-18T14:44:18.166939Z",
     "start_time": "2018-02-18T14:44:18.147414Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "180218OutputslsqpGBP5.xlsx\n"
     ]
    }
   ],
   "source": [
    "name = 'GBP'\n",
    "name_L = 'Output'.join((date.today().strftime('%y%m%d'),op_methods+name+'5.xlsx'))\n",
    "writer = pd.ExcelWriter(name_L)\n",
    "print(name_L)\n",
    "output.to_excel(writer, 'Sheet1')\n",
    "writer.save()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Verify likelihood function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-18T13:13:08.785441Z",
     "start_time": "2018-02-18T13:13:08.118693Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  3.61949616e-04   1.22233618e-03   4.11949060e-03   1.37878801e-02\n",
      "   4.50930968e-02   1.36730002e-01   3.30164995e-01   4.87000000e-01]\n",
      "0.487\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "5704.7398250465258"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "op_methods = 'lbfgsb'\n",
    "row = 0\n",
    "dum_data = raw[row]\n",
    "returns = np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "returns = returns\n",
    "a = returns.to_frame()\n",
    "data = a['Column2']\n",
    "\n",
    "MSM_likelihood_new(1.353,3.38,0.974,0.550, 8, data*100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fit data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## FIT for forecast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T13:01:48.241597Z",
     "start_time": "2018-02-25T13:01:42.818285Z"
    },
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-39-67ab611e71c4>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     16\u001b[0m \u001b[1;31m# fit params\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     17\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 18\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mMSM_fitdata\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata_fit\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkbar\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mLB\u001b[0m \u001b[1;33m,\u001b[0m\u001b[0mUB\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mop_methods\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstartingvals\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     19\u001b[0m \u001b[1;31m#re2 = MSM_likelihood_new(result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value,  kbar, data_fit)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     20\u001b[0m \u001b[0mrez\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-5-44fb0eecbb52>\u001b[0m in \u001b[0;36mMSM_fitdata\u001b[1;34m(data, kbar, LB, UB, op_methods, startingvals)\u001b[0m\n\u001b[0;32m     13\u001b[0m     \"\"\"\n\u001b[0;32m     14\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 15\u001b[1;33m     \u001b[0minput_param\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mLLS\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mMSM_starting_values\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstartingvals\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkbar\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     16\u001b[0m         \u001b[1;31m# print('LL = %8.4f' % LLS.loc[0, 'LL'])\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     17\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-3-9741c784fec9>\u001b[0m in \u001b[0;36mMSM_starting_values\u001b[1;34m(data, startingvals, kbar)\u001b[0m\n\u001b[0;32m     45\u001b[0m             a_m0 = fminbound(MSM_likelihood_new, 1.2, 1.8,\n\u001b[0;32m     46\u001b[0m                              \u001b[0margs\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mg\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msigma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkbar\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 47\u001b[1;33m                              xtol=1e-05, maxfun=500, full_output=True)  # , disp=3)\n\u001b[0m\u001b[0;32m     48\u001b[0m             \u001b[0mLL_storage\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mloc\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mLL_storage\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'LL'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0ma_m0\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     49\u001b[0m             \u001b[0mLL_storage\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mloc\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mLL_storage\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'b'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\optimize.py\u001b[0m in \u001b[0;36mfminbound\u001b[1;34m(func, x1, x2, args, xtol, maxfun, full_output, disp)\u001b[0m\n\u001b[0;32m   1617\u001b[0m                'disp': disp}\n\u001b[0;32m   1618\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1619\u001b[1;33m     \u001b[0mres\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_minimize_scalar_bounded\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mx1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0moptions\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1620\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mfull_output\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1621\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mres\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'x'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mres\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'fun'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mres\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'status'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mres\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'nfev'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\optimize.py\u001b[0m in \u001b[0;36m_minimize_scalar_bounded\u001b[1;34m(func, bounds, args, xatol, maxiter, disp, **unknown_options)\u001b[0m\n\u001b[0;32m   1714\u001b[0m         \u001b[0msi\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msign\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrat\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mrat\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1715\u001b[0m         \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mxf\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0msi\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mnumpy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtol1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1716\u001b[1;33m         \u001b[0mfu\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1717\u001b[0m         \u001b[0mnum\u001b[0m \u001b[1;33m+=\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1718\u001b[0m         \u001b[0mfmin_data\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mnum\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfu\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-4-1ee095e55a09>\u001b[0m in \u001b[0;36mMSM_likelihood_new\u001b[1;34m(*args)\u001b[0m\n\u001b[0;32m    105\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mg_m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    106\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 107\u001b[1;33m     \u001b[0mA\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mgamma\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtransition_mat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mA_temp\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mgamma_k\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkbar\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    108\u001b[0m     \u001b[0mg_m\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mgofm\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mm0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkbar\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    109\u001b[0m     \u001b[0mT\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-4-1ee095e55a09>\u001b[0m in \u001b[0;36mtransition_mat\u001b[1;34m(A_temp, b, gamma_k, kbar)\u001b[0m\n\u001b[0;32m     77\u001b[0m         \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m2\u001b[0m \u001b[1;33m**\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mkbar\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     78\u001b[0m             \u001b[1;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m2\u001b[0m \u001b[1;33m**\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mkbar\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 79\u001b[1;33m                 \u001b[0mA\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mkbar2\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mi\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mj\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mprob\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mkbar2\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mA\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mj\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     80\u001b[0m                 \u001b[0mA\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mkbar2\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mj\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mA\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mkbar2\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mi\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mj\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     81\u001b[0m                 \u001b[0mA\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkbar2\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mi\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mA\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mkbar2\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mi\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mj\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "row = 0\n",
    "op_methods = 'slsqp'\n",
    "predict_period = 1\n",
    "kbar = 10\n",
    "\n",
    "starting_index = 3000\n",
    "dum_data = raw[row]\n",
    "returns = np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "a = returns.to_frame()\n",
    "data = a['Column2']*100\n",
    "LB = [1, 1, 0.001, 0.0001]\n",
    "UB = [1.99, 50, 0.99999, 50]\n",
    "startingvals = []\n",
    "data_fit = data[:starting_index]\n",
    "\n",
    "# fit params\n",
    "\n",
    "result = MSM_fitdata(data_fit, kbar, LB ,UB,op_methods, startingvals)\n",
    "#re2 = MSM_likelihood_new(result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value,  kbar, data_fit)\n",
    "rez = result.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Chain forecast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T13:45:00.509471Z",
     "start_time": "2018-02-25T13:32:16.793191Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         LL    b     g        m sigma\n",
      "0  -350.937  1.5   0.1  1.66302   NaN\n",
      "1  -350.937    3   0.1  1.66302   NaN\n",
      "2  -350.937    6   0.1  1.66302   NaN\n",
      "3  -350.937   20   0.1  1.66302   NaN\n",
      "4  -279.652  1.5   0.5  1.71289   NaN\n",
      "5  -279.652    3   0.5  1.71289   NaN\n",
      "6  -279.652    6   0.5  1.71289   NaN\n",
      "7  -279.652   20   0.5  1.71289   NaN\n",
      "8  -213.158  1.5  0.99  1.69334   NaN\n",
      "9  -213.158    3  0.99  1.69334   NaN\n",
      "10 -213.158    6  0.99  1.69334   NaN\n",
      "11 -213.158   20  0.99  1.69334   NaN\n",
      "==========init params=========\n",
      "m0 =   1.6630\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.2372\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.6694\n",
      "b =   1.5000\n",
      "gamma_k =   0.0720\n",
      "sigma =   0.2572\n",
      "\n",
      "\n",
      "         LL    b         g        m sigma\n",
      "0  -421.009  1.5  0.072032  1.54328   NaN\n",
      "1  -421.009  1.5  0.072032  1.54328   NaN\n",
      "2  -421.009  1.5  0.072032  1.54328   NaN\n",
      "3  -421.009  1.5  0.072032  1.54328   NaN\n",
      "4  -318.226  1.5  0.531016  1.60865   NaN\n",
      "5  -318.226  1.5  0.531016  1.60865   NaN\n",
      "6  -318.226  1.5  0.531016  1.60865   NaN\n",
      "7  -318.226  1.5  0.531016  1.60865   NaN\n",
      "8  -233.999  1.5      0.99  1.60174   NaN\n",
      "9  -233.999  1.5      0.99  1.60174   NaN\n",
      "10 -233.999  1.5      0.99  1.60174   NaN\n",
      "11 -233.999  1.5      0.99  1.60174   NaN\n",
      "==========init params=========\n",
      "m0 =   1.5433\n",
      "b =   1.5000\n",
      "gamma_k =   0.0720\n",
      "sigma =   0.2572\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.5701\n",
      "b =   5.7991\n",
      "gamma_k =   0.0923\n",
      "sigma =   0.2805\n",
      "\n",
      "\n",
      "         LL        b          g        m sigma\n",
      "0  -424.227  5.79914  0.0923191  1.58295   NaN\n",
      "1  -424.089  4.36609  0.0923191  1.57819   NaN\n",
      "2  -423.865  2.93305  0.0923191   1.4686   NaN\n",
      "3  -420.378      1.5  0.0923191  1.48005   NaN\n",
      "4  -415.474  5.79914    0.54116  1.51482   NaN\n",
      "5   -405.59  4.36609    0.54116  1.51994   NaN\n",
      "6  -382.934  2.93305    0.54116   1.5299   NaN\n",
      "7  -339.631  5.79914       0.99  1.54829   NaN\n",
      "8  -326.458      1.5    0.54116  1.55325   NaN\n",
      "9  -312.177  4.36609       0.99  1.55741   NaN\n",
      "10 -270.856  2.93305       0.99  1.56592   NaN\n",
      "11 -223.722      1.5       0.99  1.56506   NaN\n",
      "==========init params=========\n",
      "m0 =   1.5830\n",
      "b =   5.7991\n",
      "gamma_k =   0.0923\n",
      "sigma =   0.2805\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.5391\n",
      "b =   5.8917\n",
      "gamma_k =   0.1180\n",
      "sigma =   0.2315\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0  -435.116  2.96391   0.11799   1.4262   NaN\n",
      "1  -434.263  5.89174  0.553995  1.45088   NaN\n",
      "2  -431.658      1.5   0.11799  1.41377   NaN\n",
      "3  -430.851  4.42783   0.11799   1.4346   NaN\n",
      "4  -430.379  4.42783  0.553995  1.43788   NaN\n",
      "5  -426.668  5.89174   0.11799  1.44581   NaN\n",
      "6  -419.359  2.96391  0.553995  1.42218   NaN\n",
      "7  -404.619  5.89174      0.99  1.42716   NaN\n",
      "8  -388.544  4.42783      0.99   1.4293   NaN\n",
      "9  -363.875      1.5  0.553995  1.43045   NaN\n",
      "10 -346.557  2.96391      0.99  1.43462   NaN\n",
      "11 -265.443      1.5      0.99  1.41946   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4262\n",
      "b =   2.9639\n",
      "gamma_k =   0.1180\n",
      "sigma =   0.2315\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.4986\n",
      "b =   3.4864\n",
      "gamma_k =   0.1087\n",
      "sigma =   0.3010\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0  -434.466  2.16215   0.10867  1.41391   NaN\n",
      "1   -433.39  2.82429   0.10867  1.41517   NaN\n",
      "2  -431.406  3.48644   0.10867   1.4167   NaN\n",
      "3  -430.064      1.5   0.10867  1.41374   NaN\n",
      "4  -426.753  3.48644  0.549335  1.42454   NaN\n",
      "5  -420.802  2.82429  0.549335  1.42078   NaN\n",
      "6  -402.411  2.16215  0.549335  1.43043   NaN\n",
      "7  -381.602  3.48644      0.99  1.44243   NaN\n",
      "8  -351.713  2.82429      0.99  1.45708   NaN\n",
      "9  -349.931      1.5  0.549335  1.45825   NaN\n",
      "10 -298.527  2.16215      0.99  1.47795   NaN\n",
      "11 -226.901      1.5      0.99   1.4932   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4139\n",
      "b =   2.1621\n",
      "gamma_k =   0.1087\n",
      "sigma =   0.3010\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.3917\n",
      "b =   2.6397\n",
      "gamma_k =   0.2394\n",
      "sigma =   0.2385\n",
      "\n",
      "\n",
      "         LL        b        g        m sigma\n",
      "0  -439.933  2.25982  0.23938  1.36234   NaN\n",
      "1  -439.504  1.87991  0.23938  1.34979   NaN\n",
      "2  -438.313  2.63973  0.23938  1.37905   NaN\n",
      "3  -435.985  2.63973  0.61469  1.35453   NaN\n",
      "4  -432.259      1.5  0.23938  1.34359   NaN\n",
      "5  -431.026  2.25982  0.61469  1.35042   NaN\n",
      "6  -418.246  1.87991  0.61469  1.35065   NaN\n",
      "7  -401.861  2.63973     0.99  1.35714   NaN\n",
      "8  -387.465      1.5  0.61469  1.35889   NaN\n",
      "9  -379.619  2.25982     0.99  1.36244   NaN\n",
      "10 -342.034  1.87991     0.99  1.36776   NaN\n",
      "11 -292.334      1.5     0.99  1.36468   NaN\n",
      "==========init params=========\n",
      "m0 =   1.3623\n",
      "b =   2.2598\n",
      "gamma_k =   0.2394\n",
      "sigma =   0.2385\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.3558\n",
      "b =   2.1694\n",
      "gamma_k =   0.2541\n",
      "sigma =   0.2294\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   -440.35  1.94626  0.254084  1.33044   NaN\n",
      "1  -439.933  1.72313  0.254084  1.32111   NaN\n",
      "2  -439.221  2.16939  0.254084  1.34204   NaN\n",
      "3  -435.924  2.16939  0.622042  1.32312   NaN\n",
      "4   -435.77      1.5  0.254084  1.31514   NaN\n",
      "5  -431.118  1.94626  0.622042  1.32032   NaN\n",
      "6  -420.864  1.72313  0.622042  1.32011   NaN\n",
      "7  -400.801      1.5  0.622042  1.32391   NaN\n",
      "8  -397.857  2.16939      0.99  1.32722   NaN\n",
      "9  -377.314  1.94626      0.99  1.33041   NaN\n",
      "10 -347.156  1.72313      0.99   1.3329   NaN\n",
      "11 -309.265      1.5      0.99  1.33067   NaN\n",
      "==========init params=========\n",
      "m0 =   1.3304\n",
      "b =   1.9463\n",
      "gamma_k =   0.2541\n",
      "sigma =   0.2294\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.3268\n",
      "b =   1.8993\n",
      "gamma_k =   0.2685\n",
      "sigma =   0.2283\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0  -440.448  1.76618  0.268459  1.30752   NaN\n",
      "1  -440.176  1.63309  0.268459  1.30043   NaN\n",
      "2  -439.872  1.89927  0.268459  1.31681   NaN\n",
      "3  -438.105      1.5  0.268459  1.29553   NaN\n",
      "4  -435.356  1.89927   0.62923  1.30025   NaN\n",
      "5  -431.255  1.76618   0.62923   1.2986   NaN\n",
      "6  -423.887  1.63309   0.62923  1.29857   NaN\n",
      "7  -411.602      1.5   0.62923  1.30063   NaN\n",
      "8  -394.047  1.89927      0.99  1.30662   NaN\n",
      "9  -377.012  1.76618      0.99   1.3091   NaN\n",
      "10 -354.549  1.63309      0.99  1.31106   NaN\n",
      "11 -327.384      1.5      0.99  1.31088   NaN\n",
      "==========init params=========\n",
      "m0 =   1.3075\n",
      "b =   1.7662\n",
      "gamma_k =   0.2685\n",
      "sigma =   0.2283\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.3059\n",
      "b =   1.7351\n",
      "gamma_k =   0.2729\n",
      "sigma =   0.2308\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0  -440.645   1.6567  0.272882  1.29195   NaN\n",
      "1  -440.557  1.57835  0.272882  1.28648   NaN\n",
      "2  -440.378  1.73505  0.272882  1.29851   NaN\n",
      "3  -439.808      1.5  0.272882  1.28217   NaN\n",
      "4  -435.051  1.73505  0.631441  1.28301   NaN\n",
      "5  -432.085   1.6567  0.631441  1.28206   NaN\n",
      "6  -427.484  1.57835  0.631441  1.28203   NaN\n",
      "7  -420.711      1.5  0.631441  1.28305   NaN\n",
      "8  -392.013  1.73505      0.99   1.2913   NaN\n",
      "9  -379.425   1.6567      0.99  1.29336   NaN\n",
      "10 -364.101  1.57835      0.99  1.29523   NaN\n",
      "11 -346.216      1.5      0.99  1.29633   NaN\n",
      "==========init params=========\n",
      "m0 =   1.2919\n",
      "b =   1.6567\n",
      "gamma_k =   0.2729\n",
      "sigma =   0.2308\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.2915\n",
      "b =   1.6467\n",
      "gamma_k =   0.2796\n",
      "sigma =   0.2346\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0  -440.839  1.54889  0.279606  1.27595   NaN\n",
      "1  -440.772  1.59778  0.279606  1.27992   NaN\n",
      "2   -440.65      1.5  0.279606  1.27252   NaN\n",
      "3  -440.544  1.64667  0.279606  1.28449   NaN\n",
      "4  -435.498  1.64667  0.634803  1.26989   NaN\n",
      "5  -433.604  1.59778  0.634803  1.26914   NaN\n",
      "6  -430.933  1.54889  0.634803   1.2689   NaN\n",
      "7  -427.292      1.5  0.634803  1.26922   NaN\n",
      "8  -394.492  1.64667      0.99  1.27855   NaN\n",
      "9  -385.725  1.59778      0.99  1.28032   NaN\n",
      "10 -375.506  1.54889      0.99  1.28208   NaN\n",
      "11 -363.841      1.5      0.99  1.28367   NaN\n",
      "==========init params=========\n",
      "m0 =   1.2759\n",
      "b =   1.5489\n",
      "gamma_k =   0.2796\n",
      "sigma =   0.2346\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.2766\n",
      "b =   1.5693\n",
      "gamma_k =   0.2899\n",
      "sigma =   0.2345\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "row = 3\n",
    "op_methods = 'slsqp'\n",
    "predict_period = 1\n",
    "\n",
    "starting_index = 3000\n",
    "dum_data = raw[row]\n",
    "returns = np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "a = returns.to_frame()\n",
    "data = a['Column2']*100\n",
    "LB = [1, 1, 0.001, 0.0001]\n",
    "UB = [1.99, 50, 0.99999, 50]\n",
    "startingvals = []\n",
    "data_fit = data[:starting_index]\n",
    "\n",
    "# fit params\n",
    "\n",
    "for i in range(0,10):\n",
    "    kbar = i+1\n",
    "    if kbar >1 and bool(result):\n",
    "        startingvals = [result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value]\n",
    "    result = MSM_fitdata(data_fit, kbar, LB ,UB,op_methods, startingvals)\n",
    "    rez = result.params\n",
    "    re2 = MSM_likelihood_new(result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,\n",
    "                             result.params['sigma'].value,  kbar, data_fit\n",
    "                            )\n",
    "    output.loc[i,\"LL\"] = re2\n",
    "    for element in result.params:\n",
    "        output.loc[i,element] = result.params[element].value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T13:45:05.041413Z",
     "start_time": "2018-02-25T13:45:00.509471Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pi_mat, A, sigma, s = MSM_likelihood_wantto_forecast(rez, kbar, data, predict_period)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PICKLE for import/export model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### save"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T13:45:05.057040Z",
     "start_time": "2018-02-25T13:45:05.041413Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "180225_10slsqpDM.pkl\n"
     ]
    }
   ],
   "source": [
    "import pickle\n",
    "from datetime import date\n",
    "# obj0, obj1, obj2 are created here...\n",
    "\n",
    "data_name = 'DM'\n",
    "model_name = ''.join((date.today().strftime('%y%m%d'),\"_\"+ str(kbar)+ op_methods+ str(data_name) + '.pkl'))\n",
    "# Saving the objects:\n",
    "with open(model_name, 'wb') as f: \n",
    "    pickle.dump(result.params, f)\n",
    "    print(model_name)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-18T12:33:28.237599Z",
     "start_time": "2018-02-18T12:33:28.235001Z"
    }
   },
   "source": [
    "### load"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T12:56:19.895957Z",
     "start_time": "2018-02-25T12:56:19.864746Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# import pickle\n",
    "# # Getting back the objects:\n",
    "with open('180219_10slsqpDM.pkl', 'rb') as f:  # Python 3: open(..., 'rb')\n",
    "    rez_2 = pickle.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T12:56:26.620705Z",
     "start_time": "2018-02-25T12:56:26.605035Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Parameters([('m0', <Parameter 'm0', 1.4569812297413369, bounds=[1:1.99]>),\n",
       "            ('b', <Parameter 'b', 2.5397755601437977, bounds=[1:50]>),\n",
       "            ('gamma_k',\n",
       "             <Parameter 'gamma_k', 0.83829678924064988, bounds=[0.001:0.99999]>),\n",
       "            ('sigma',\n",
       "             <Parameter 'sigma', 0.41064273031690784, bounds=[0.0001:50]>)])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rez"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T12:56:37.394826Z",
     "start_time": "2018-02-25T12:56:37.364030Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Parameters([('m0', <Parameter 'm0', 1.6299929540997213, bounds=[1:1.99]>),\n",
       "            ('b', <Parameter 'b', 4.4117265184781624, bounds=[1:50]>),\n",
       "            ('gamma_k',\n",
       "             <Parameter 'gamma_k', 0.70285396272487677, bounds=[0.001:0.99999]>),\n",
       "            ('sigma',\n",
       "             <Parameter 'sigma', 0.58279795462479345, bounds=[0.0001:50]>)])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rez_2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## forecast process 1 day "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T13:45:08.760598Z",
     "start_time": "2018-02-25T13:45:05.057040Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# df for OLS\n",
    "Pdict = df()\n",
    "Pdict[\"vol\"] = []\n",
    "predict_period = 1\n",
    "\n",
    "vol = np.ones((predict_period,1))\n",
    "vol = vol.astype(float)\n",
    "for i in range(starting_index,len(pi_mat)-1):\n",
    "    \n",
    "    state_now = pi_mat[i , :]\n",
    "    for t in range(0,predict_period):\n",
    "        vol[t,0] = np.inner(np.matmul(state_now, np.linalg.matrix_power(A, t+1)),s[1,:])\n",
    "    Pdict.loc[i,\"vol\"] = sum(vol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T13:45:08.791810Z",
     "start_time": "2018-02-25T13:45:08.760598Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>vol</th>\n",
       "      <th>real</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>3000</th>\n",
       "      <td>0.263898</td>\n",
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       "      <td>0.082254</td>\n",
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       "      <td>0.278031</td>\n",
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       "      <th>3017</th>\n",
       "      <td>0.241098</td>\n",
       "      <td>0.046368</td>\n",
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       "    <tr>\n",
       "      <th>3018</th>\n",
       "      <td>0.241762</td>\n",
       "      <td>0.267886</td>\n",
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       "    <tr>\n",
       "      <th>3019</th>\n",
       "      <td>0.297877</td>\n",
       "      <td>0.001298</td>\n",
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       "    <tr>\n",
       "      <th>3020</th>\n",
       "      <td>0.273634</td>\n",
       "      <td>0.016840</td>\n",
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       "      <td>0.000208</td>\n",
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       "      <td>0.235482</td>\n",
       "      <td>0.373813</td>\n",
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       "      <th>3023</th>\n",
       "      <td>0.318034</td>\n",
       "      <td>0.185925</td>\n",
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       "      <td>0.329380</td>\n",
       "      <td>0.011683</td>\n",
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       "      <td>0.303038</td>\n",
       "      <td>0.241545</td>\n",
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       "    <tr>\n",
       "      <th>3026</th>\n",
       "      <td>0.333336</td>\n",
       "      <td>0.015190</td>\n",
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       "    <tr>\n",
       "      <th>3027</th>\n",
       "      <td>0.307450</td>\n",
       "      <td>0.001316</td>\n",
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       "      <th>3028</th>\n",
       "      <td>0.280038</td>\n",
       "      <td>0.021034</td>\n",
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       "    <tr>\n",
       "      <th>3029</th>\n",
       "      <td>0.263685</td>\n",
       "      <td>0.015157</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>7018</th>\n",
       "      <td>0.253018</td>\n",
       "      <td>0.704806</td>\n",
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       "    <tr>\n",
       "      <th>7019</th>\n",
       "      <td>0.379132</td>\n",
       "      <td>0.001052</td>\n",
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       "    <tr>\n",
       "      <th>7020</th>\n",
       "      <td>0.344104</td>\n",
       "      <td>0.033054</td>\n",
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       "    <tr>\n",
       "      <th>7021</th>\n",
       "      <td>0.320981</td>\n",
       "      <td>0.028600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7022</th>\n",
       "      <td>0.300669</td>\n",
       "      <td>0.022453</td>\n",
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       "    <tr>\n",
       "      <th>7023</th>\n",
       "      <td>0.281889</td>\n",
       "      <td>0.006116</td>\n",
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       "    <tr>\n",
       "      <th>7024</th>\n",
       "      <td>0.259458</td>\n",
       "      <td>0.086195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7025</th>\n",
       "      <td>0.272671</td>\n",
       "      <td>0.068127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7026</th>\n",
       "      <td>0.274935</td>\n",
       "      <td>0.001062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7027</th>\n",
       "      <td>0.253293</td>\n",
       "      <td>0.180310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7028</th>\n",
       "      <td>0.292113</td>\n",
       "      <td>0.002099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7029</th>\n",
       "      <td>0.269459</td>\n",
       "      <td>0.000171</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7030</th>\n",
       "      <td>0.247582</td>\n",
       "      <td>0.185670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7031</th>\n",
       "      <td>0.289836</td>\n",
       "      <td>0.026569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7032</th>\n",
       "      <td>0.275146</td>\n",
       "      <td>0.000681</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7033</th>\n",
       "      <td>0.253192</td>\n",
       "      <td>0.173770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7034</th>\n",
       "      <td>0.289558</td>\n",
       "      <td>0.000169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7035</th>\n",
       "      <td>0.266415</td>\n",
       "      <td>0.013708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7036</th>\n",
       "      <td>0.250501</td>\n",
       "      <td>0.046029</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7037</th>\n",
       "      <td>0.250118</td>\n",
       "      <td>0.427438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7038</th>\n",
       "      <td>0.333693</td>\n",
       "      <td>0.026060</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7039</th>\n",
       "      <td>0.311130</td>\n",
       "      <td>0.040215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7040</th>\n",
       "      <td>0.295953</td>\n",
       "      <td>0.032934</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7041</th>\n",
       "      <td>0.281563</td>\n",
       "      <td>0.390272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7042</th>\n",
       "      <td>0.347317</td>\n",
       "      <td>0.324377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7043</th>\n",
       "      <td>0.372995</td>\n",
       "      <td>0.188564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7044</th>\n",
       "      <td>0.372369</td>\n",
       "      <td>0.117160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7045</th>\n",
       "      <td>0.361371</td>\n",
       "      <td>0.002117</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7046</th>\n",
       "      <td>0.328045</td>\n",
       "      <td>0.461645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7047</th>\n",
       "      <td>0.389005</td>\n",
       "      <td>0.292996</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>4048 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           vol      real\n",
       "3000  0.263898  0.238701\n",
       "3001  0.303271  0.003385\n",
       "3002  0.278490  0.005282\n",
       "3003  0.256471  0.053919\n",
       "3004  0.256532  0.480795\n",
       "3005  0.342735  0.063307\n",
       "3006  0.325556  0.000206\n",
       "3007  0.295745  0.000000\n",
       "3008  0.268269  0.070364\n",
       "3009  0.272440  0.082254\n",
       "3010  0.278031  0.043450\n",
       "3011  0.270168  0.005181\n",
       "3012  0.250052  0.013288\n",
       "3013  0.235893  0.053337\n",
       "3014  0.241437  0.020853\n",
       "3015  0.232276  0.119524\n",
       "3016  0.259332  0.004185\n",
       "3017  0.241098  0.046368\n",
       "3018  0.241762  0.267886\n",
       "3019  0.297877  0.001298\n",
       "3020  0.273634  0.016840\n",
       "3021  0.257019  0.000208\n",
       "3022  0.235482  0.373813\n",
       "3023  0.318034  0.185925\n",
       "3024  0.329380  0.011683\n",
       "3025  0.303038  0.241545\n",
       "3026  0.333336  0.015190\n",
       "3027  0.307450  0.001316\n",
       "3028  0.280038  0.021034\n",
       "3029  0.263685  0.015157\n",
       "...        ...       ...\n",
       "7018  0.253018  0.704806\n",
       "7019  0.379132  0.001052\n",
       "7020  0.344104  0.033054\n",
       "7021  0.320981  0.028600\n",
       "7022  0.300669  0.022453\n",
       "7023  0.281889  0.006116\n",
       "7024  0.259458  0.086195\n",
       "7025  0.272671  0.068127\n",
       "7026  0.274935  0.001062\n",
       "7027  0.253293  0.180310\n",
       "7028  0.292113  0.002099\n",
       "7029  0.269459  0.000171\n",
       "7030  0.247582  0.185670\n",
       "7031  0.289836  0.026569\n",
       "7032  0.275146  0.000681\n",
       "7033  0.253192  0.173770\n",
       "7034  0.289558  0.000169\n",
       "7035  0.266415  0.013708\n",
       "7036  0.250501  0.046029\n",
       "7037  0.250118  0.427438\n",
       "7038  0.333693  0.026060\n",
       "7039  0.311130  0.040215\n",
       "7040  0.295953  0.032934\n",
       "7041  0.281563  0.390272\n",
       "7042  0.347317  0.324377\n",
       "7043  0.372995  0.188564\n",
       "7044  0.372369  0.117160\n",
       "7045  0.361371  0.002117\n",
       "7046  0.328045  0.461645\n",
       "7047  0.389005  0.292996\n",
       "\n",
       "[4048 rows x 2 columns]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns = np.log(1+dum_data['Column2'].pct_change().dropna())\n",
    "a = returns.to_frame()\n",
    "data = a['Column2']*100\n",
    "rsq = data[starting_index-2:].shift(-predict_period)\n",
    "dfrsq = rsq.to_frame()\n",
    "Pdict['real']=dfrsq**2\n",
    "Pdict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T12:57:10.189422Z",
     "start_time": "2018-02-25T12:57:10.158170Z"
    },
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2999    0.127299\n",
       "3000    0.001578\n",
       "3001    0.311108\n",
       "3002    1.419519\n",
       "3003    0.303802\n",
       "3004    0.954062\n",
       "3005    0.434004\n",
       "3006    2.071969\n",
       "3007    2.371633\n",
       "3008    1.316507\n",
       "3009    0.055844\n",
       "3010    0.759151\n",
       "3011    0.177033\n",
       "3012    0.110339\n",
       "3013    0.014044\n",
       "3014    1.389559\n",
       "3015    0.006108\n",
       "3016    2.407529\n",
       "3017    0.331438\n",
       "3018    5.251678\n",
       "3019    0.620733\n",
       "3020    0.000000\n",
       "3021    0.024187\n",
       "3022    1.013223\n",
       "3023    0.214667\n",
       "3024    1.810096\n",
       "3025    0.118497\n",
       "3026    0.005876\n",
       "3027    0.442175\n",
       "3028    1.173901\n",
       "          ...   \n",
       "7269    0.057591\n",
       "7270    0.009201\n",
       "7271    0.018822\n",
       "7272    0.020750\n",
       "7273    0.091236\n",
       "7274    0.048297\n",
       "7275    0.078888\n",
       "7276    0.015181\n",
       "7277    0.141379\n",
       "7278    0.041991\n",
       "7279    0.000421\n",
       "7280    0.013533\n",
       "7281    0.045148\n",
       "7282    0.016974\n",
       "7283    0.005678\n",
       "7284    0.001687\n",
       "7285    0.269198\n",
       "7286    0.016716\n",
       "7287    0.000740\n",
       "7288    0.031190\n",
       "7289    0.101417\n",
       "7290    0.336519\n",
       "7291    0.001131\n",
       "7292    0.533191\n",
       "7293    0.001113\n",
       "7294    0.210995\n",
       "7295    0.143872\n",
       "7296    2.082160\n",
       "7297    0.198803\n",
       "7298    0.068664\n",
       "Name: Column2, Length: 4300, dtype: float64"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rsq = data[starting_index-2:]**2\n",
    "rsq"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### stats model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-19T10:16:27.802961Z",
     "start_time": "2018-02-19T10:16:27.787289Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T13:45:08.838691Z",
     "start_time": "2018-02-25T13:45:08.791810Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dataset = 3\n",
      "m0  =   1.2766\n",
      "b  =   1.5693\n",
      "gamma_k  =   0.2899\n",
      "sigma  =   0.2345\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   real   R-squared:                       0.044\n",
      "Model:                            OLS   Adj. R-squared:                  0.044\n",
      "Method:                 Least Squares   F-statistic:                     185.1\n",
      "Date:                Sun, 25 Feb 2018   Prob (F-statistic):           3.05e-41\n",
      "Time:                        14:45:08   Log-Likelihood:                 976.51\n",
      "No. Observations:                4048   AIC:                            -1949.\n",
      "Df Residuals:                    4046   BIC:                            -1936.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         -0.0524      0.011     -4.835      0.000      -0.074      -0.031\n",
      "x1             0.5348      0.039     13.603      0.000       0.458       0.612\n",
      "==============================================================================\n",
      "Omnibus:                     5091.925   Durbin-Watson:                   1.996\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):           966124.741\n",
      "Skew:                           6.780   Prob(JB):                         0.00\n",
      "Kurtosis:                      77.459   Cond. No.                         14.1\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "MODEL MSE 0.0361582766155\n",
      "MODEL TSE 0.0378026954695\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "print('dataset = %1.0f' %row)\n",
    "\n",
    "for ele in rez:\n",
    "    print(ele,' = %8.4f'  %rez[ele].value)\n",
    "x = Pdict.loc[:,'vol'].values.reshape(len(Pdict),1)\n",
    "y = Pdict['real']\n",
    "\n",
    "x2 = sm.add_constant(x)\n",
    "est = sm.OLS(y, x2)\n",
    "est2 = est.fit()\n",
    "print(est2.summary())\n",
    "# print(\"MODEL MSE\",est2.mse_model)\n",
    "print(\"MODEL MSE\",est2.mse_resid)\n",
    "print(\"MODEL TSE\",est2.mse_total)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXPORT Result!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-18T19:37:16.759213Z",
     "start_time": "2018-02-18T19:37:16.755637Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# output = df()\n",
    "# "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-18T19:45:18.078391Z",
     "start_time": "2018-02-18T19:45:18.049708Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for element in result.params:\n",
    "    output.loc[row,element] = result.params[element].value\n",
    "\n",
    "output.loc[row,'Slope'] = sum(regr.coef_)\n",
    "output.loc[row,'intercept'] =  regr.intercept_\n",
    "output.loc[row,'MSE'] = mean_squared_error(y, x)\n",
    "output.loc[row,'R_sq'] = r2_score(y, x)\n",
    "\n",
    "writer = pd.ExcelWriter('Output'.join((date.today().strftime('%y%m%d'),'ALL_REG.xlsx')))\n",
    "output.to_excel(writer, 'Sheet1')\n",
    "writer.save()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-18T19:07:29.384315Z",
     "start_time": "2018-02-18T19:07:29.379988Z"
    },
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Parameters([('m0', <Parameter 'm0', 1.629998096335135, bounds=[1:1.99]>),\n",
       "            ('b', <Parameter 'b', 4.4120315416646161, bounds=[1:50]>),\n",
       "            ('gamma_k',\n",
       "             <Parameter 'gamma_k', 0.70287857197217063, bounds=[0.001:0.99999]>),\n",
       "            ('sigma',\n",
       "             <Parameter 'sigma', 0.58282108145794298, bounds=[0.0001:50]>)])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T13:01:11.015243Z",
     "start_time": "2018-02-25T13:01:10.983946Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>m0</th>\n",
       "      <th>b</th>\n",
       "      <th>gamma_k</th>\n",
       "      <th>sigma</th>\n",
       "      <th>LL</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.856799</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>0.151344</td>\n",
       "      <td>0.559417</td>\n",
       "      <td>2165.156704</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.790297</td>\n",
       "      <td>18.353692</td>\n",
       "      <td>0.223294</td>\n",
       "      <td>0.518750</td>\n",
       "      <td>1994.989617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.760918</td>\n",
       "      <td>14.145956</td>\n",
       "      <td>0.332085</td>\n",
       "      <td>0.448827</td>\n",
       "      <td>1918.480683</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.704834</td>\n",
       "      <td>5.141529</td>\n",
       "      <td>0.170362</td>\n",
       "      <td>0.540188</td>\n",
       "      <td>1886.691143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.636330</td>\n",
       "      <td>5.037106</td>\n",
       "      <td>0.384254</td>\n",
       "      <td>0.447685</td>\n",
       "      <td>1877.105656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.600150</td>\n",
       "      <td>5.596331</td>\n",
       "      <td>0.688778</td>\n",
       "      <td>0.524212</td>\n",
       "      <td>1872.450342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.559214</td>\n",
       "      <td>4.162739</td>\n",
       "      <td>0.673908</td>\n",
       "      <td>0.435483</td>\n",
       "      <td>1869.788388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.512173</td>\n",
       "      <td>3.358684</td>\n",
       "      <td>0.800145</td>\n",
       "      <td>0.436961</td>\n",
       "      <td>1870.498799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.484956</td>\n",
       "      <td>2.810734</td>\n",
       "      <td>0.792318</td>\n",
       "      <td>0.423587</td>\n",
       "      <td>1870.388228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.456981</td>\n",
       "      <td>2.539776</td>\n",
       "      <td>0.838297</td>\n",
       "      <td>0.410643</td>\n",
       "      <td>1870.705819</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         m0          b   gamma_k     sigma           LL\n",
       "0  1.856799   1.500000  0.151344  0.559417  2165.156704\n",
       "1  1.790297  18.353692  0.223294  0.518750  1994.989617\n",
       "2  1.760918  14.145956  0.332085  0.448827  1918.480683\n",
       "3  1.704834   5.141529  0.170362  0.540188  1886.691143\n",
       "4  1.636330   5.037106  0.384254  0.447685  1877.105656\n",
       "5  1.600150   5.596331  0.688778  0.524212  1872.450342\n",
       "6  1.559214   4.162739  0.673908  0.435483  1869.788388\n",
       "7  1.512173   3.358684  0.800145  0.436961  1870.498799\n",
       "8  1.484956   2.810734  0.792318  0.423587  1870.388228\n",
       "9  1.456981   2.539776  0.838297  0.410643  1870.705819"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Gold Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:06:25.573397Z",
     "start_time": "2018-02-28T14:06:23.759927Z"
    },
    "deletable": false,
    "editable": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WEHu3QYMWTM+92qoz7qWAZk9edSaF4ycTM3/91ert3hnkj9l/sJXyolE72LXe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\nJAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x231a10b1a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "GVZ = pd.read_excel('data_GVZ_GLD_long.xlsx','GVZ')\n",
    "GLD = pd.read_excel('data_GVZ_GLD_long.xlsx','GLD')\n",
    "\n",
    "GLD_r = GLD.loc[:,'log return'].dropna()\n",
    "GLD_date = GLD.loc[:,'Date'].dropna()\n",
    "GLD_data = GLD.loc[:,'index'].dropna()\n",
    "\n",
    "plt.plot(GLD_date.iloc[:-1],200*GLD_r)\n",
    "plt.plot(GLD_date,GLD_data)\n",
    "plt.title('GLD data')\n",
    "\n",
    "\n",
    "data = GLD_r[::-1]\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## output "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:06:28.292996Z",
     "start_time": "2018-02-28T14:06:28.262136Z"
    },
    "collapsed": true,
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "output = df()\n",
    "output[\"m0\"] = []\n",
    "output[\"b\"] = []\n",
    "output[\"gamma_k\"]=[]\n",
    "output[\"sigma\"] = []\n",
    "output[\"LL\"] = []\n",
    "result = []\n",
    "\n",
    "startingvals = []#[1.2, 1.2, 0.5 , 1.2 ]\n",
    "LB = [1, 1, 0.001, 0.0001]\n",
    "UB = [1.99, 50, 0.99999, 50]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:06:36.466204Z",
     "start_time": "2018-02-28T14:06:32.231463Z"
    },
    "deletable": false,
    "editable": false
   },
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-17-effda8ec5cef>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      7\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mkbar\u001b[0m \u001b[1;33m>\u001b[0m\u001b[1;36m1\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0mbool\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m         \u001b[0mstartingvals\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'm0'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'b'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'gamma_k'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'sigma'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 9\u001b[1;33m     \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mMSM_fitdata\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkbar\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mLB\u001b[0m \u001b[1;33m,\u001b[0m\u001b[0mUB\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mop_methods\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstartingvals\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     10\u001b[0m     \u001b[0mre2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mMSM_likelihood_new\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'm0'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'b'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'gamma_k'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'sigma'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m,\u001b[0m  \u001b[0mkbar\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdata2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     11\u001b[0m     \u001b[0moutput\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mloc\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m\"LL\"\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mre2\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-5-44fb0eecbb52>\u001b[0m in \u001b[0;36mMSM_fitdata\u001b[1;34m(data, kbar, LB, UB, op_methods, startingvals)\u001b[0m\n\u001b[0;32m     13\u001b[0m     \"\"\"\n\u001b[0;32m     14\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 15\u001b[1;33m     \u001b[0minput_param\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mLLS\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mMSM_starting_values\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstartingvals\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkbar\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     16\u001b[0m         \u001b[1;31m# print('LL = %8.4f' % LLS.loc[0, 'LL'])\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     17\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-3-9741c784fec9>\u001b[0m in \u001b[0;36mMSM_starting_values\u001b[1;34m(data, startingvals, kbar)\u001b[0m\n\u001b[0;32m     45\u001b[0m             a_m0 = fminbound(MSM_likelihood_new, 1.2, 1.8,\n\u001b[0;32m     46\u001b[0m                              \u001b[0margs\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mg\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msigma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkbar\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 47\u001b[1;33m                              xtol=1e-05, maxfun=500, full_output=True)  # , disp=3)\n\u001b[0m\u001b[0;32m     48\u001b[0m             \u001b[0mLL_storage\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mloc\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mLL_storage\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'LL'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0ma_m0\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     49\u001b[0m             \u001b[0mLL_storage\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mloc\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mLL_storage\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'b'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\optimize.py\u001b[0m in \u001b[0;36mfminbound\u001b[1;34m(func, x1, x2, args, xtol, maxfun, full_output, disp)\u001b[0m\n\u001b[0;32m   1617\u001b[0m                'disp': disp}\n\u001b[0;32m   1618\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1619\u001b[1;33m     \u001b[0mres\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_minimize_scalar_bounded\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mx1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0moptions\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1620\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mfull_output\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1621\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mres\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'x'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mres\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'fun'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mres\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'status'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mres\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'nfev'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\optimize.py\u001b[0m in \u001b[0;36m_minimize_scalar_bounded\u001b[1;34m(func, bounds, args, xatol, maxiter, disp, **unknown_options)\u001b[0m\n\u001b[0;32m   1714\u001b[0m         \u001b[0msi\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msign\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrat\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mrat\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1715\u001b[0m         \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mxf\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0msi\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mnumpy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtol1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1716\u001b[1;33m         \u001b[0mfu\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1717\u001b[0m         \u001b[0mnum\u001b[0m \u001b[1;33m+=\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1718\u001b[0m         \u001b[0mfmin_data\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mnum\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfu\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-4-1ee095e55a09>\u001b[0m in \u001b[0;36mMSM_likelihood_new\u001b[1;34m(*args)\u001b[0m\n\u001b[0;32m    128\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    129\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mT\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 130\u001b[1;33m         \u001b[0mpiA\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpi_mat\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mA\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    131\u001b[0m         \u001b[0mC\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmultiply\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mw_t\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpiA\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    132\u001b[0m         \u001b[0mft\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mC\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "op_methods = 'slsqp'\n",
    "data2 = data#[::-1]\n",
    "startingvals = []\n",
    "\n",
    "for i in range(0,10):\n",
    "    kbar = i+1\n",
    "    if kbar >1 and bool(result):\n",
    "        startingvals = [result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value]\n",
    "    result = MSM_fitdata(data, kbar, LB ,UB,op_methods, startingvals)\n",
    "    re2 = MSM_likelihood_new(result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value,  kbar, data2)\n",
    "    output.loc[i,\"LL\"] = re2\n",
    "    for element in result.params:\n",
    "        output.loc[i,element] = result.params[element].value\n",
    "        \n",
    "writer = pd.ExcelWriter('Output'.join((date.today().strftime('%y%m%d'),op_methods+'GLDvaryk.xlsx')))\n",
    "output.to_excel(writer, 'Sheet1')\n",
    "writer.save()\n",
    "        \n",
    "output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GLD Forecast"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### drop index "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:06:43.920795Z",
     "start_time": "2018-02-28T14:06:43.874408Z"
    },
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "GVZ_date = GVZ.loc[:,'Date'].dropna()\n",
    "GVZ_data = GVZ.loc[:,'index'].dropna()\n",
    "GLD_date = GLD.loc[:,'Date'].dropna()\n",
    "GLD_data = GLD.loc[:,'index'].dropna()\n",
    "\n",
    "# GVZ/GLD use for regression (new -> old)\n",
    "GVZ_date = GVZ_date.drop(GVZ_date.index[0])\n",
    "GVZ_date = GVZ_date.reset_index(drop=True)\n",
    "GVZ_data = GVZ_data.reset_index(drop=True)\n",
    "\n",
    "GLD_data = GLD_data.drop(GLD_date.index[0])\n",
    "GLD_data = GLD_data.reset_index(drop=True)\n",
    "GLD_date = GLD_date.drop(GLD_date.index[0])\n",
    "GLD_date = GLD_date.drop(GLD_date.index[len(GLD_date)-1])\n",
    "GLD_date = GLD_date.reset_index(drop=True)\n",
    "\n",
    "# all to df\n",
    "df_reg = GVZ_date.to_frame()\n",
    "df_reg[\"GVZ\"] = GVZ_data\n",
    "df_reg[\"GLD\"] = GLD_data\n",
    "\n",
    "# [old -> new]\n",
    "df_reg = df_reg[::-1]\n",
    "# df_reg\n",
    "\n",
    "# New data drop the first (last date) because there are no GVZ data\n",
    "# data use for MSM function (old -> new)\n",
    "data = GLD_r\n",
    "data = data.drop(data.index[len(data)-1])\n",
    "data = data.reset_index(drop=True)\n",
    "data_fit = data.drop(data.index[0:len(df_reg)])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## chain forecast"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### param"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:35:57.133150Z",
     "start_time": "2018-02-28T14:35:57.102236Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "op_methods = 'slsqp'\n",
    "predict_period = 1\n",
    "kbar = 10\n",
    "LB = [1, 1, 0.001, 0.0001]\n",
    "UB = [1.99, 50, 0.99999, 50]\n",
    "startingvals = []"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### fit param"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T19:13:10.973882Z",
     "start_time": "2018-02-25T18:41:27.407285Z"
    },
    "code_folding": [],
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         LL    b     g        m sigma\n",
      "0   5287.55  1.5   0.1  1.76859   NaN\n",
      "1   5287.55    3   0.1  1.76859   NaN\n",
      "2   5287.55    6   0.1  1.76859   NaN\n",
      "3   5287.55   20   0.1  1.76859   NaN\n",
      "4   5582.06  1.5   0.5  1.79999   NaN\n",
      "5   5582.06    3   0.5  1.79999   NaN\n",
      "6   5582.06    6   0.5  1.79999   NaN\n",
      "7   5582.06   20   0.5  1.79999   NaN\n",
      "8   5890.46  1.5  0.99  1.79999   NaN\n",
      "9   5890.46    3  0.99  1.79999   NaN\n",
      "10  5890.46    6  0.99  1.79999   NaN\n",
      "11  5890.46   20  0.99  1.79999   NaN\n",
      "==========init params=========\n",
      "m0 =   1.7686\n",
      "b =   1.5000\n",
      "gamma_k =   0.1000\n",
      "sigma =   0.5476\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.7919\n",
      "b =   1.5000\n",
      "gamma_k =   0.0475\n",
      "sigma =   0.6704\n",
      "\n",
      "\n",
      "         LL    b          g        m sigma\n",
      "0   4874.16  1.5  0.0474686  1.68317   NaN\n",
      "1   4874.16  1.5  0.0474686  1.68317   NaN\n",
      "2   4874.16  1.5  0.0474686  1.68317   NaN\n",
      "3   4874.16  1.5  0.0474686  1.68317   NaN\n",
      "4   5274.58  1.5   0.518734   1.7791   NaN\n",
      "5   5274.58  1.5   0.518734   1.7791   NaN\n",
      "6   5274.58  1.5   0.518734   1.7791   NaN\n",
      "7   5274.58  1.5   0.518734   1.7791   NaN\n",
      "8    5704.4  1.5       0.99  1.79953   NaN\n",
      "9    5704.4  1.5       0.99  1.79953   NaN\n",
      "10   5704.4  1.5       0.99  1.79953   NaN\n",
      "11   5704.4  1.5       0.99  1.79953   NaN\n",
      "==========init params=========\n",
      "m0 =   1.6832\n",
      "b =   1.5000\n",
      "gamma_k =   0.0475\n",
      "sigma =   0.6704\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.7135\n",
      "b =  13.6114\n",
      "gamma_k =   0.1490\n",
      "sigma =   0.6136\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   4678.74  9.57426  0.148971  1.62391   NaN\n",
      "1   4679.09  13.6114  0.148971  1.62624   NaN\n",
      "2    4686.8  5.53713  0.148971  1.62202   NaN\n",
      "3   4711.09  13.6114  0.569485  1.64087   NaN\n",
      "4   4728.06  9.57426  0.569485  1.64024   NaN\n",
      "5   4783.47  5.53713  0.569485  1.64177   NaN\n",
      "6   4797.41      1.5  0.148971  1.62294   NaN\n",
      "7   4839.58  13.6114      0.99  1.65304   NaN\n",
      "8   4904.47  9.57426      0.99  1.65691   NaN\n",
      "9   5069.41  5.53713      0.99  1.66781   NaN\n",
      "10  5154.18      1.5  0.569485  1.66866   NaN\n",
      "11  5572.03      1.5      0.99  1.68441   NaN\n",
      "==========init params=========\n",
      "m0 =   1.6239\n",
      "b =   9.5743\n",
      "gamma_k =   0.1490\n",
      "sigma =   0.6136\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.6462\n",
      "b =  10.8101\n",
      "gamma_k =   0.1358\n",
      "sigma =   0.7044\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   4605.28  10.8101  0.562894  1.61358   NaN\n",
      "1   4616.61   7.7067  0.135787  1.59533   NaN\n",
      "2   4620.22  10.8101  0.135787  1.60025   NaN\n",
      "3   4621.54  4.60335  0.135787  1.58491   NaN\n",
      "4   4621.55   7.7067  0.562894  1.60461   NaN\n",
      "5   4679.43  4.60335  0.562894  1.59537   NaN\n",
      "6   4694.72  10.8101      0.99  1.60505   NaN\n",
      "7   4734.71      1.5  0.135787  1.57649   NaN\n",
      "8   4749.18   7.7067      0.99  1.60537   NaN\n",
      "9   4908.02  4.60335      0.99  1.61845   NaN\n",
      "10  5106.53      1.5  0.562894  1.62946   NaN\n",
      "11  5589.54      1.5      0.99  1.66461   NaN\n",
      "==========init params=========\n",
      "m0 =   1.6136\n",
      "b =  10.8101\n",
      "gamma_k =   0.5629\n",
      "sigma =   0.7044\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.6218\n",
      "b =  24.9210\n",
      "gamma_k =   0.7492\n",
      "sigma =   0.6756\n",
      "\n",
      "\n",
      "         LL       b         g        m sigma\n",
      "0   4565.47  17.114  0.749154  1.54166   NaN\n",
      "1    4568.2  17.114  0.869577  1.54467   NaN\n",
      "2   4569.75  24.921  0.869577  1.54492   NaN\n",
      "3   4571.13   9.307  0.749154  1.53987   NaN\n",
      "4   4571.72  24.921  0.749154  1.54187   NaN\n",
      "5   4579.41   9.307  0.869577  1.54523   NaN\n",
      "6   4582.93  24.921      0.99  1.55227   NaN\n",
      "7   4586.27  17.114      0.99  1.54835   NaN\n",
      "8   4608.29   9.307      0.99  1.54337   NaN\n",
      "9   5150.45     1.5  0.749154  1.57687   NaN\n",
      "10  5268.38     1.5  0.869577  1.58754   NaN\n",
      "11  5493.39     1.5      0.99  1.59878   NaN\n",
      "==========init params=========\n",
      "m0 =   1.5417\n",
      "b =  17.1140\n",
      "gamma_k =   0.7492\n",
      "sigma =   0.6756\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.5437\n",
      "b =  14.1371\n",
      "gamma_k =   0.6941\n",
      "sigma =   0.6959\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   4551.62  9.92473  0.842031  1.51052   NaN\n",
      "1   4555.26  9.92473      0.99  1.51262   NaN\n",
      "2   4556.15  14.1371      0.99  1.51355   NaN\n",
      "3   4557.04  5.71237  0.694061  1.50264   NaN\n",
      "4   4557.95  9.92473  0.694061  1.52109   NaN\n",
      "5   4560.06  14.1371  0.842031  1.53011   NaN\n",
      "6   4560.49  5.71237  0.842031  1.50217   NaN\n",
      "7   4567.78  14.1371  0.694061  1.54962   NaN\n",
      "8   4590.72  5.71237      0.99  1.50122   NaN\n",
      "9   5033.96      1.5  0.694061  1.53053   NaN\n",
      "10  5162.11      1.5  0.842031  1.54537   NaN\n",
      "11   5431.9      1.5      0.99  1.56463   NaN\n",
      "==========init params=========\n",
      "m0 =   1.5105\n",
      "b =   9.9247\n",
      "gamma_k =   0.8420\n",
      "sigma =   0.6959\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.4969\n",
      "b =   8.3168\n",
      "gamma_k =   0.8821\n",
      "sigma =   0.6258\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   4544.33   6.0445  0.936038  1.45892   NaN\n",
      "1   4544.97   6.0445  0.882077  1.46506   NaN\n",
      "2   4546.26   6.0445      0.99  1.45848   NaN\n",
      "3   4547.58  8.31675      0.99    1.474   NaN\n",
      "4   4547.97  8.31675  0.936038   1.4811   NaN\n",
      "5   4549.15  8.31675  0.882077  1.48115   NaN\n",
      "6   4561.12  3.77225  0.882077  1.44812   NaN\n",
      "7   4567.58  3.77225  0.936038  1.44875   NaN\n",
      "8   4588.07  3.77225      0.99  1.44988   NaN\n",
      "9   5068.23      1.5  0.882077  1.48362   NaN\n",
      "10   5140.5      1.5  0.936038  1.48976   NaN\n",
      "11  5290.34      1.5      0.99  1.49842   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4589\n",
      "b =   6.0445\n",
      "gamma_k =   0.9360\n",
      "sigma =   0.6258\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.4644\n",
      "b =   6.5047\n",
      "gamma_k =   0.9236\n",
      "sigma =   0.5546\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   4538.78  4.83649  0.956819  1.42565   NaN\n",
      "1   4539.18  4.83649  0.923638  1.42629   NaN\n",
      "2   4539.59  4.83649      0.99   1.4247   NaN\n",
      "3   4542.07  6.50473      0.99  1.43381   NaN\n",
      "4    4544.2  6.50473  0.956819  1.43447   NaN\n",
      "5   4546.43  6.50473  0.923638  1.45996   NaN\n",
      "6    4553.9  3.16824  0.923638  1.40695   NaN\n",
      "7    4558.4  3.16824  0.956819  1.40753   NaN\n",
      "8   4570.77  3.16824      0.99  1.40826   NaN\n",
      "9   5000.56      1.5  0.923638  1.42899   NaN\n",
      "10  5055.47      1.5  0.956819  1.43267   NaN\n",
      "11  5164.81      1.5      0.99  1.43772   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4256\n",
      "b =   4.8365\n",
      "gamma_k =   0.9568\n",
      "sigma =   0.5546\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.4409\n",
      "b =   5.4425\n",
      "gamma_k =   0.9350\n",
      "sigma =   0.6451\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   4533.76  4.12831  0.962476  1.40943   NaN\n",
      "1    4534.4  4.12831      0.99  1.40751   NaN\n",
      "2   4534.41  4.12831  0.934952   1.4098   NaN\n",
      "3   4537.07  5.44247      0.99  1.41876   NaN\n",
      "4   4540.22  5.44247  0.962476  1.42025   NaN\n",
      "5   4542.77  5.44247  0.934952  1.44731   NaN\n",
      "6      4552  2.81416  0.934952  1.39249   NaN\n",
      "7   4556.59  2.81416  0.962476  1.39313   NaN\n",
      "8   4568.27  2.81416      0.99  1.39466   NaN\n",
      "9   4978.56      1.5  0.934952  1.43213   NaN\n",
      "10   5026.9      1.5  0.962476  1.43716   NaN\n",
      "11  5121.25      1.5      0.99  1.44533   NaN\n",
      "==========init params=========\n",
      "m0 =   1.4094\n",
      "b =   4.1283\n",
      "gamma_k =   0.9625\n",
      "sigma =   0.6451\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.4036\n",
      "b =   4.2899\n",
      "gamma_k =   0.9861\n",
      "sigma =   0.5902\n",
      "\n",
      "\n",
      "         LL        b         g        m sigma\n",
      "0   4531.07  3.35994  0.986113  1.37706   NaN\n",
      "1   4531.11  3.35994  0.988057  1.37694   NaN\n",
      "2   4531.19  3.35994      0.99   1.3768   NaN\n",
      "3   4535.93  4.28991      0.99   1.3856   NaN\n",
      "4   4536.37  4.28991  0.988057  1.38577   NaN\n",
      "5    4537.2  4.28991  0.986113  1.41042   NaN\n",
      "6   4562.08  2.42997  0.986113  1.36407   NaN\n",
      "7   4563.37  2.42997  0.988057  1.36424   NaN\n",
      "8   4564.89  2.42997      0.99  1.36443   NaN\n",
      "9   4981.71      1.5  0.986113   1.3989   NaN\n",
      "10  4990.73      1.5  0.988057  1.39962   NaN\n",
      "11  5001.06      1.5      0.99  1.40043   NaN\n",
      "==========init params=========\n",
      "m0 =   1.3771\n",
      "b =   3.3599\n",
      "gamma_k =   0.9861\n",
      "sigma =   0.5902\n",
      "\n",
      "\n",
      " ==========fitted results==========\n",
      "optimization method = slsqp\n",
      "m0 =   1.3763\n",
      "b =   3.5314\n",
      "gamma_k =   0.9943\n",
      "sigma =   0.5659\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# fit params\n",
    "for i in range(0,10):\n",
    "    kbar = i+1\n",
    "    if kbar >1 and bool(result):\n",
    "        startingvals = [result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,result.params['sigma'].value]\n",
    "    result = MSM_fitdata(data_fit, kbar, LB ,UB,op_methods, startingvals)\n",
    "    rez = result.params\n",
    "    re2 = MSM_likelihood_new(result.params['m0'].value,result.params['b'].value,result.params['gamma_k'].value,\n",
    "                             result.params['sigma'].value,  kbar, data_fit\n",
    "                            )\n",
    "    output.loc[i,\"LL\"] = re2\n",
    "    for element in result.params:\n",
    "        output.loc[i,element] = result.params[element].value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## save params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T19:13:17.912353Z",
     "start_time": "2018-02-25T19:13:17.881101Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "180225_10slsqpGLD.pkl\n"
     ]
    }
   ],
   "source": [
    "import pickle\n",
    "from datetime import date\n",
    "# obj0, obj1, obj2 are created here...\n",
    "\n",
    "data_name = 'GLD'\n",
    "model_name = ''.join((date.today().strftime('%y%m%d'),\"_\"+ str(kbar)+ op_methods+ str(data_name) + '.pkl'))\n",
    "# Saving the objects:\n",
    "with open(model_name, 'wb') as f: \n",
    "    pickle.dump(result.params, f)\n",
    "    print(model_name)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### load params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:07:38.984956Z",
     "start_time": "2018-02-28T14:07:38.938564Z"
    },
    "collapsed": true,
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "import pickle\n",
    "# # Getting back the objects:\n",
    "with open('180225_10slsqpGLD.pkl', 'rb') as f:  # Python 3: open(..., 'rb')\n",
    "    rez_2 = pickle.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:07:46.033450Z",
     "start_time": "2018-02-28T14:07:46.017783Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rez = rez_2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## get forecast params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:39:28.853221Z",
     "start_time": "2018-02-28T14:39:21.805007Z"
    }
   },
   "outputs": [],
   "source": [
    "predict_period = -1\n",
    "pi_mat, A, sigma, s = MSM_likelihood_wantto_forecast(rez, kbar, data, predict_period)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## forecast 1 day"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-25T19:53:32.622062Z",
     "start_time": "2018-02-25T19:53:32.575184Z"
    },
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>GVZ</th>\n",
       "      <th>GLD</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2444</th>\n",
       "      <td>2008-06-03</td>\n",
       "      <td>22.89</td>\n",
       "      <td>859.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2443</th>\n",
       "      <td>2008-06-04</td>\n",
       "      <td>22.69</td>\n",
       "      <td>887.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2442</th>\n",
       "      <td>2008-06-05</td>\n",
       "      <td>22.78</td>\n",
       "      <td>907.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2441</th>\n",
       "      <td>2008-06-06</td>\n",
       "      <td>23.60</td>\n",
       "      <td>913.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2440</th>\n",
       "      <td>2008-06-09</td>\n",
       "      <td>24.47</td>\n",
       "      <td>849.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2439</th>\n",
       "      <td>2008-06-10</td>\n",
       "      <td>25.39</td>\n",
       "      <td>833.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2438</th>\n",
       "      <td>2008-06-11</td>\n",
       "      <td>25.36</td>\n",
       "      <td>836.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2437</th>\n",
       "      <td>2008-06-12</td>\n",
       "      <td>25.04</td>\n",
       "      <td>846.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2436</th>\n",
       "      <td>2008-06-13</td>\n",
       "      <td>24.94</td>\n",
       "      <td>804.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2435</th>\n",
       "      <td>2008-06-16</td>\n",
       "      <td>24.98</td>\n",
       "      <td>783.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2434</th>\n",
       "      <td>2008-06-17</td>\n",
       "      <td>24.45</td>\n",
       "      <td>796.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2433</th>\n",
       "      <td>2008-06-18</td>\n",
       "      <td>23.93</td>\n",
       "      <td>771.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2432</th>\n",
       "      <td>2008-06-19</td>\n",
       "      <td>24.33</td>\n",
       "      <td>730.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2431</th>\n",
       "      <td>2008-06-20</td>\n",
       "      <td>26.22</td>\n",
       "      <td>721.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2430</th>\n",
       "      <td>2008-06-23</td>\n",
       "      <td>27.18</td>\n",
       "      <td>734.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2429</th>\n",
       "      <td>2008-06-24</td>\n",
       "      <td>26.79</td>\n",
       "      <td>730.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2428</th>\n",
       "      <td>2008-06-25</td>\n",
       "      <td>26.78</td>\n",
       "      <td>746.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2427</th>\n",
       "      <td>2008-06-26</td>\n",
       "      <td>27.33</td>\n",
       "      <td>754.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2426</th>\n",
       "      <td>2008-06-27</td>\n",
       "      <td>26.47</td>\n",
       "      <td>738.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2425</th>\n",
       "      <td>2008-06-30</td>\n",
       "      <td>26.92</td>\n",
       "      <td>724.55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2424</th>\n",
       "      <td>2008-07-01</td>\n",
       "      <td>27.64</td>\n",
       "      <td>723.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2423</th>\n",
       "      <td>2008-07-02</td>\n",
       "      <td>27.54</td>\n",
       "      <td>763.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2422</th>\n",
       "      <td>2008-07-03</td>\n",
       "      <td>26.85</td>\n",
       "      <td>740.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2421</th>\n",
       "      <td>2008-07-07</td>\n",
       "      <td>26.59</td>\n",
       "      <td>732.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2420</th>\n",
       "      <td>2008-07-08</td>\n",
       "      <td>26.12</td>\n",
       "      <td>736.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2419</th>\n",
       "      <td>2008-07-09</td>\n",
       "      <td>26.09</td>\n",
       "      <td>746.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2418</th>\n",
       "      <td>2008-07-10</td>\n",
       "      <td>26.79</td>\n",
       "      <td>731.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2417</th>\n",
       "      <td>2008-07-11</td>\n",
       "      <td>33.32</td>\n",
       "      <td>712.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2416</th>\n",
       "      <td>2008-07-14</td>\n",
       "      <td>31.09</td>\n",
       "      <td>736.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2415</th>\n",
       "      <td>2008-07-15</td>\n",
       "      <td>30.40</td>\n",
       "      <td>742.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>2018-01-05</td>\n",
       "      <td>11.26</td>\n",
       "      <td>1320.47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>2018-01-08</td>\n",
       "      <td>11.19</td>\n",
       "      <td>1312.78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>2018-01-09</td>\n",
       "      <td>10.79</td>\n",
       "      <td>1316.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>2018-01-10</td>\n",
       "      <td>10.79</td>\n",
       "      <td>1322.37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>2018-01-11</td>\n",
       "      <td>10.96</td>\n",
       "      <td>1337.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>2018-01-12</td>\n",
       "      <td>11.62</td>\n",
       "      <td>1340.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>2018-01-16</td>\n",
       "      <td>12.09</td>\n",
       "      <td>1338.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>2018-01-17</td>\n",
       "      <td>11.77</td>\n",
       "      <td>1327.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>2018-01-18</td>\n",
       "      <td>12.26</td>\n",
       "      <td>1327.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>2018-01-19</td>\n",
       "      <td>11.43</td>\n",
       "      <td>1331.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>2018-01-22</td>\n",
       "      <td>11.66</td>\n",
       "      <td>1333.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>2018-01-23</td>\n",
       "      <td>11.72</td>\n",
       "      <td>1341.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>2018-01-24</td>\n",
       "      <td>13.38</td>\n",
       "      <td>1358.47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>2018-01-25</td>\n",
       "      <td>13.04</td>\n",
       "      <td>1348.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>2018-01-26</td>\n",
       "      <td>12.98</td>\n",
       "      <td>1349.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2018-01-29</td>\n",
       "      <td>13.25</td>\n",
       "      <td>1340.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2018-01-30</td>\n",
       "      <td>13.86</td>\n",
       "      <td>1338.51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>2018-01-31</td>\n",
       "      <td>12.97</td>\n",
       "      <td>1345.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2018-02-01</td>\n",
       "      <td>12.32</td>\n",
       "      <td>1348.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2018-02-02</td>\n",
       "      <td>13.11</td>\n",
       "      <td>1332.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2018-02-05</td>\n",
       "      <td>14.35</td>\n",
       "      <td>1339.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2018-02-06</td>\n",
       "      <td>13.80</td>\n",
       "      <td>1324.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2018-02-07</td>\n",
       "      <td>13.62</td>\n",
       "      <td>1318.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2018-02-08</td>\n",
       "      <td>14.85</td>\n",
       "      <td>1318.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2018-02-09</td>\n",
       "      <td>14.93</td>\n",
       "      <td>1316.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2018-02-12</td>\n",
       "      <td>14.37</td>\n",
       "      <td>1322.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2018-02-13</td>\n",
       "      <td>14.07</td>\n",
       "      <td>1329.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2018-02-14</td>\n",
       "      <td>14.97</td>\n",
       "      <td>1350.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2018-02-15</td>\n",
       "      <td>15.03</td>\n",
       "      <td>1353.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2018-02-16</td>\n",
       "      <td>13.96</td>\n",
       "      <td>1347.10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2445 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           Date    GVZ      GLD\n",
       "2444 2008-06-03  22.89   859.75\n",
       "2443 2008-06-04  22.69   887.10\n",
       "2442 2008-06-05  22.78   907.62\n",
       "2441 2008-06-06  23.60   913.25\n",
       "2440 2008-06-09  24.47   849.85\n",
       "2439 2008-06-10  25.39   833.05\n",
       "2438 2008-06-11  25.36   836.70\n",
       "2437 2008-06-12  25.04   846.90\n",
       "2436 2008-06-13  24.94   804.60\n",
       "2435 2008-06-16  24.98   783.35\n",
       "2434 2008-06-17  24.45   796.90\n",
       "2433 2008-06-18  23.93   771.65\n",
       "2432 2008-06-19  24.33   730.45\n",
       "2431 2008-06-20  26.22   721.45\n",
       "2430 2008-06-23  27.18   734.75\n",
       "2429 2008-06-24  26.79   730.80\n",
       "2428 2008-06-25  26.78   746.95\n",
       "2427 2008-06-26  27.33   754.95\n",
       "2426 2008-06-27  26.47   738.13\n",
       "2425 2008-06-30  26.92   724.55\n",
       "2424 2008-07-01  27.64   723.45\n",
       "2423 2008-07-02  27.54   763.25\n",
       "2422 2008-07-03  26.85   740.35\n",
       "2421 2008-07-07  26.59   732.85\n",
       "2420 2008-07-08  26.12   736.65\n",
       "2419 2008-07-09  26.09   746.20\n",
       "2418 2008-07-10  26.79   731.70\n",
       "2417 2008-07-11  33.32   712.30\n",
       "2416 2008-07-14  31.09   736.50\n",
       "2415 2008-07-15  30.40   742.10\n",
       "...         ...    ...      ...\n",
       "29   2018-01-05  11.26  1320.47\n",
       "28   2018-01-08  11.19  1312.78\n",
       "27   2018-01-09  10.79  1316.92\n",
       "26   2018-01-10  10.79  1322.37\n",
       "25   2018-01-11  10.96  1337.95\n",
       "24   2018-01-12  11.62  1340.06\n",
       "23   2018-01-16  12.09  1338.43\n",
       "22   2018-01-17  11.77  1327.15\n",
       "21   2018-01-18  12.26  1327.12\n",
       "20   2018-01-19  11.43  1331.85\n",
       "19   2018-01-22  11.66  1333.62\n",
       "18   2018-01-23  11.72  1341.18\n",
       "17   2018-01-24  13.38  1358.47\n",
       "16   2018-01-25  13.04  1348.01\n",
       "15   2018-01-26  12.98  1349.70\n",
       "14   2018-01-29  13.25  1340.31\n",
       "13   2018-01-30  13.86  1338.51\n",
       "12   2018-01-31  12.97  1345.15\n",
       "11   2018-02-01  12.32  1348.70\n",
       "10   2018-02-02  13.11  1332.90\n",
       "9    2018-02-05  14.35  1339.68\n",
       "8    2018-02-06  13.80  1324.10\n",
       "7    2018-02-07  13.62  1318.52\n",
       "6    2018-02-08  14.85  1318.77\n",
       "5    2018-02-09  14.93  1316.15\n",
       "4    2018-02-12  14.37  1322.76\n",
       "3    2018-02-13  14.07  1329.63\n",
       "2    2018-02-14  14.97  1350.67\n",
       "1    2018-02-15  15.03  1353.70\n",
       "0    2018-02-16  13.96  1347.10\n",
       "\n",
       "[2445 rows x 3 columns]"
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_reg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:15:06.554033Z",
     "start_time": "2018-02-28T14:15:06.538789Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8610"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "starting_index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T15:43:35.010046Z",
     "start_time": "2018-02-28T15:43:34.978961Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8610"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(data)-len(df_reg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "\\ if startindex = 10,000) \\\\\n",
    "\\ time use = t*(t-1)/2*37 \\\\\n",
    "\\ period = 4 , time = 195 \\\\\n",
    "\\ // O(PERIOD^2) \\\\\n",
    "\\end{align}\n",
    "\n",
    "if add data startindex = 9,000 => data set = 2,055 (increase around 2x from 1,055)\n",
    "time est => 380\n",
    "// O(2N)\n",
    "\n",
    "start index = 10,000\n",
    "p = 10\n",
    "time est => 1,665\n",
    "TIme use => 1,193\n",
    "\n",
    "if startindex = 8,610\n",
    "=> dataset = 2,445 => 2.5 multiple\n",
    "=> period  = 20\n",
    "=> base time use from period = 7,030 sec => 2 hrs\n",
    "=> time use after dataset = 2*2.5 = 5 hrs??\n",
    "\n",
    "time use = p*(p-1)\n",
    "\\begin{align}\n",
    "\\dot{x} & = \\sigma(y-x) \\\\\n",
    "\\dot{y} & = \\rho x - y - xz \\\\\n",
    "\\dot{z} & = -\\beta z + xy\n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T16:07:03.064000Z",
     "start_time": "2018-02-28T15:47:09.349267Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TIME : 1193.69911\n"
     ]
    }
   ],
   "source": [
    "# df for OLS\n",
    "starting_index = 10000#len(data)-len(df_reg)\n",
    "predict_period = 10\n",
    "from time import time\n",
    "\n",
    "t1 = time()\n",
    "Pdict = df()\n",
    "Pdict[\"vol\"] = []\n",
    "df_reg[\"vol\"] = 0.\n",
    "\n",
    "\n",
    "vol = np.ones((predict_period,1))\n",
    "vol = vol.astype(float)\n",
    "for i in range(starting_index,len(pi_mat)-1):\n",
    "    \n",
    "    state_now = pi_mat[i , :]\n",
    "    for t in range(0,predict_period):\n",
    "        vol[t,0] = np.inner(np.matmul(state_now, np.linalg.matrix_power(A, t+1)),s[1,:])\n",
    "    df_reg.loc[i-starting_index,\"vol\"] = sum(vol)\n",
    "print(\"TIME : %2.5f\" %(time() - t1)) \n",
    "#     Pdict.loc[i,\"vol\"] = sum(vol)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T16:10:57.743299Z",
     "start_time": "2018-02-28T16:10:57.727672Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.69890899],\n",
       "       [ 0.68477608],\n",
       "       [ 0.67199557],\n",
       "       [ 0.66128373],\n",
       "       [ 0.65230282],\n",
       "       [ 0.64465993],\n",
       "       [ 0.63804761],\n",
       "       [ 0.63224247],\n",
       "       [ 0.62708345],\n",
       "       [ 0.622453  ]])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T15:03:26.889913Z",
     "start_time": "2018-02-28T15:03:26.732972Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.572107181703\n",
      "0.572107181703\n",
      "0.572107181703\n",
      "0.572107181703\n",
      "0.572107181703\n",
      "0.572107181703\n",
      "0.572107181703\n",
      "0.572107181703\n",
      "0.572107181703\n",
      "0.572107181703\n",
      "TIME : 0.14131\n"
     ]
    }
   ],
   "source": [
    "from time import time\n",
    "\n",
    "t1 = time()\n",
    "predict_period = 5\n",
    "i = starting_index +2\n",
    "t = predict_period\n",
    "a = np.matmul(state_now, np.linalg.matrix_power(A, t+1))\n",
    "for i in range(0,10):\n",
    "    print(np.inner(a,s[1,:]))\n",
    "print(\"TIME : %2.5f\" %(time() - t1)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T15:01:47.355285Z",
     "start_time": "2018-02-28T15:01:47.324034Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kbar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:29:31.052316Z",
     "start_time": "2018-02-28T14:29:31.036691Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:39:36.543848Z",
     "start_time": "2018-02-28T14:39:36.528224Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.69890899]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T16:17:23.772200Z",
     "start_time": "2018-02-28T16:17:22.780508Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.66880011]\n",
      " [ 0.63557156]\n",
      " [ 0.62010768]\n",
      " [ 0.61107726]\n",
      " [ 0.60523024]\n",
      " [ 0.60129086]\n",
      " [ 0.59860782]\n",
      " [ 0.59678979]\n",
      " [ 0.5955829 ]\n",
      " [ 0.59481667]]\n",
      "[ 6.1278749]\n"
     ]
    }
   ],
   "source": [
    "i = starting_index +1\n",
    "state_now = pi_mat[i , :]\n",
    "for t in range(0,predict_period):\n",
    "    vol[t,0] = np.inner(np.matmul(state_now, np.linalg.matrix_power(A, t+1)),s[1,:])\n",
    "print(vol)\n",
    "print(sum(vol))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T16:22:10.951863Z",
     "start_time": "2018-02-28T16:22:10.404895Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6584584168870049"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state_now = pi_mat[starting_index+25 , :]\n",
    "np.inner(np.matmul(state_now, np.linalg.matrix_power(A, 1000)),s[1,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T16:19:29.826132Z",
     "start_time": "2018-02-28T16:19:28.627687Z"
    }
   },
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "index 10 is out of bounds for axis 0 with size 10",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-107-bb22a32ee1ec>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mstate_now\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpi_mat\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m \u001b[1;33m,\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mpredict_period\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 5\u001b[1;33m     \u001b[0mvol\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0minner\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mstate_now\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmatrix_power\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mA\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mt\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0ms\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      6\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvol\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      7\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvol\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mIndexError\u001b[0m: index 10 is out of bounds for axis 0 with size 10"
     ]
    }
   ],
   "source": [
    "i = starting_index\n",
    "state_now = pi_mat[i , :]\n",
    "for t in range(0,predict_period):\n",
    "    vol[t,0] = np.inner(np.matmul(state_now, np.linalg.matrix_power(A, t+1)),s[1,:])\n",
    "print(vol)\n",
    "print(sum(vol))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T14:55:06.510782Z",
     "start_time": "2018-02-28T14:55:06.480129Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.69890899],\n",
       "       [ 0.68477608],\n",
       "       [ 0.67199557],\n",
       "       [ 0.66128373],\n",
       "       [ 0.65230282]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-02-28T16:15:05.408864Z",
     "start_time": "2018-02-28T16:15:05.346320Z"
    },
    "deletable": false,
    "editable": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>GVZ</th>\n",
       "      <th>GLD</th>\n",
       "      <th>vol</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2444</th>\n",
       "      <td>2008-06-03</td>\n",
       "      <td>22.89</td>\n",
       "      <td>859.75</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2443</th>\n",
       "      <td>2008-06-04</td>\n",
       "      <td>22.69</td>\n",
       "      <td>887.10</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2442</th>\n",
       "      <td>2008-06-05</td>\n",
       "      <td>22.78</td>\n",
       "      <td>907.62</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2441</th>\n",
       "      <td>2008-06-06</td>\n",
       "      <td>23.60</td>\n",
       "      <td>913.25</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2440</th>\n",
       "      <td>2008-06-09</td>\n",
       "      <td>24.47</td>\n",
       "      <td>849.85</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2439</th>\n",
       "      <td>2008-06-10</td>\n",
       "      <td>25.39</td>\n",
       "      <td>833.05</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2438</th>\n",
       "      <td>2008-06-11</td>\n",
       "      <td>25.36</td>\n",
       "      <td>836.70</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2437</th>\n",
       "      <td>2008-06-12</td>\n",
       "      <td>25.04</td>\n",
       "      <td>846.90</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2436</th>\n",
       "      <td>2008-06-13</td>\n",
       "      <td>24.94</td>\n",
       "      <td>804.60</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2435</th>\n",
       "      <td>2008-06-16</td>\n",
       "      <td>24.98</td>\n",
       "      <td>783.35</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2434</th>\n",
       "      <td>2008-06-17</td>\n",
       "      <td>24.45</td>\n",
       "      <td>796.90</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2433</th>\n",
       "      <td>2008-06-18</td>\n",
       "      <td>23.93</td>\n",
       "      <td>771.65</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2432</th>\n",
       "      <td>2008-06-19</td>\n",
       "      <td>24.33</td>\n",
       "      <td>730.45</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2431</th>\n",
       "      <td>2008-06-20</td>\n",
       "      <td>26.22</td>\n",
       "      <td>721.45</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2430</th>\n",
       "      <td>2008-06-23</td>\n",
       "      <td>27.18</td>\n",
       "      <td>734.75</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2429</th>\n",
       "      <td>2008-06-24</td>\n",
       "      <td>26.79</td>\n",
       "      <td>730.80</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2428</th>\n",
       "      <td>2008-06-25</td>\n",
       "      <td>26.78</td>\n",
       "      <td>746.95</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2427</th>\n",
       "      <td>2008-06-26</td>\n",
       "      <td>27.33</td>\n",
       "      <td>754.95</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2426</th>\n",
       "      <td>2008-06-27</td>\n",
       "      <td>26.47</td>\n",
       "      <td>738.13</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2425</th>\n",
       "      <td>2008-06-30</td>\n",
       "      <td>26.92</td>\n",
       "      <td>724.55</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2424</th>\n",
       "      <td>2008-07-01</td>\n",
       "      <td>27.64</td>\n",
       "      <td>723.45</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2423</th>\n",
       "      <td>2008-07-02</td>\n",
       "      <td>27.54</td>\n",
       "      <td>763.25</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2422</th>\n",
       "      <td>2008-07-03</td>\n",
       "      <td>26.85</td>\n",
       "      <td>740.35</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2421</th>\n",
       "      <td>2008-07-07</td>\n",
       "      <td>26.59</td>\n",
       "      <td>732.85</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2420</th>\n",
       "      <td>2008-07-08</td>\n",
       "      <td>26.12</td>\n",
       "      <td>736.65</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2419</th>\n",
       "      <td>2008-07-09</td>\n",
       "      <td>26.09</td>\n",
       "      <td>746.20</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2418</th>\n",
       "      <td>2008-07-10</td>\n",
       "      <td>26.79</td>\n",
       "      <td>731.70</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2417</th>\n",
       "      <td>2008-07-11</td>\n",
       "      <td>33.32</td>\n",
       "      <td>712.30</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2416</th>\n",
       "      <td>2008-07-14</td>\n",
       "      <td>31.09</td>\n",
       "      <td>736.50</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2415</th>\n",
       "      <td>2008-07-15</td>\n",
       "      <td>30.40</td>\n",
       "      <td>742.10</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>2018-01-05</td>\n",
       "      <td>11.26</td>\n",
       "      <td>1320.47</td>\n",
       "      <td>6.696179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>2018-01-08</td>\n",
       "      <td>11.19</td>\n",
       "      <td>1312.78</td>\n",
       "      <td>5.959741</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>2018-01-09</td>\n",
       "      <td>10.79</td>\n",
       "      <td>1316.92</td>\n",
       "      <td>5.988792</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>2018-01-10</td>\n",
       "      <td>10.79</td>\n",
       "      <td>1322.37</td>\n",
       "      <td>6.180513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>2018-01-11</td>\n",
       "      <td>10.96</td>\n",
       "      <td>1337.95</td>\n",
       "      <td>6.580116</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>2018-01-12</td>\n",
       "      <td>11.62</td>\n",
       "      <td>1340.06</td>\n",
       "      <td>6.850995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>2018-01-16</td>\n",
       "      <td>12.09</td>\n",
       "      <td>1338.43</td>\n",
       "      <td>7.310829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>2018-01-17</td>\n",
       "      <td>11.77</td>\n",
       "      <td>1327.15</td>\n",
       "      <td>7.209422</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>2018-01-18</td>\n",
       "      <td>12.26</td>\n",
       "      <td>1327.12</td>\n",
       "      <td>7.706528</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>2018-01-19</td>\n",
       "      <td>11.43</td>\n",
       "      <td>1331.85</td>\n",
       "      <td>6.083269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>2018-01-22</td>\n",
       "      <td>11.66</td>\n",
       "      <td>1333.62</td>\n",
       "      <td>6.385480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>2018-01-23</td>\n",
       "      <td>11.72</td>\n",
       "      <td>1341.18</td>\n",
       "      <td>5.592633</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>2018-01-24</td>\n",
       "      <td>13.38</td>\n",
       "      <td>1358.47</td>\n",
       "      <td>5.854043</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>2018-01-25</td>\n",
       "      <td>13.04</td>\n",
       "      <td>1348.01</td>\n",
       "      <td>5.678251</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>2018-01-26</td>\n",
       "      <td>12.98</td>\n",
       "      <td>1349.70</td>\n",
       "      <td>5.728235</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2018-01-29</td>\n",
       "      <td>13.25</td>\n",
       "      <td>1340.31</td>\n",
       "      <td>5.513741</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2018-01-30</td>\n",
       "      <td>13.86</td>\n",
       "      <td>1338.51</td>\n",
       "      <td>5.851900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>2018-01-31</td>\n",
       "      <td>12.97</td>\n",
       "      <td>1345.15</td>\n",
       "      <td>4.845238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2018-02-01</td>\n",
       "      <td>12.32</td>\n",
       "      <td>1348.70</td>\n",
       "      <td>5.053575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2018-02-02</td>\n",
       "      <td>13.11</td>\n",
       "      <td>1332.90</td>\n",
       "      <td>5.244418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2018-02-05</td>\n",
       "      <td>14.35</td>\n",
       "      <td>1339.68</td>\n",
       "      <td>5.458411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2018-02-06</td>\n",
       "      <td>13.80</td>\n",
       "      <td>1324.10</td>\n",
       "      <td>5.159011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2018-02-07</td>\n",
       "      <td>13.62</td>\n",
       "      <td>1318.52</td>\n",
       "      <td>5.278265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2018-02-08</td>\n",
       "      <td>14.85</td>\n",
       "      <td>1318.77</td>\n",
       "      <td>5.465651</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2018-02-09</td>\n",
       "      <td>14.93</td>\n",
       "      <td>1316.15</td>\n",
       "      <td>5.479442</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2018-02-12</td>\n",
       "      <td>14.37</td>\n",
       "      <td>1322.76</td>\n",
       "      <td>5.783904</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2018-02-13</td>\n",
       "      <td>14.07</td>\n",
       "      <td>1329.63</td>\n",
       "      <td>5.679579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2018-02-14</td>\n",
       "      <td>14.97</td>\n",
       "      <td>1350.67</td>\n",
       "      <td>5.756023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2018-02-15</td>\n",
       "      <td>15.03</td>\n",
       "      <td>1353.70</td>\n",
       "      <td>6.127875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2018-02-16</td>\n",
       "      <td>13.96</td>\n",
       "      <td>1347.10</td>\n",
       "      <td>4.716945</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2445 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           Date    GVZ      GLD       vol\n",
       "2444 2008-06-03  22.89   859.75  0.000000\n",
       "2443 2008-06-04  22.69   887.10  0.000000\n",
       "2442 2008-06-05  22.78   907.62  0.000000\n",
       "2441 2008-06-06  23.60   913.25  0.000000\n",
       "2440 2008-06-09  24.47   849.85  0.000000\n",
       "2439 2008-06-10  25.39   833.05  0.000000\n",
       "2438 2008-06-11  25.36   836.70  0.000000\n",
       "2437 2008-06-12  25.04   846.90  0.000000\n",
       "2436 2008-06-13  24.94   804.60  0.000000\n",
       "2435 2008-06-16  24.98   783.35  0.000000\n",
       "2434 2008-06-17  24.45   796.90  0.000000\n",
       "2433 2008-06-18  23.93   771.65  0.000000\n",
       "2432 2008-06-19  24.33   730.45  0.000000\n",
       "2431 2008-06-20  26.22   721.45  0.000000\n",
       "2430 2008-06-23  27.18   734.75  0.000000\n",
       "2429 2008-06-24  26.79   730.80  0.000000\n",
       "2428 2008-06-25  26.78   746.95  0.000000\n",
       "2427 2008-06-26  27.33   754.95  0.000000\n",
       "2426 2008-06-27  26.47   738.13  0.000000\n",
       "2425 2008-06-30  26.92   724.55  0.000000\n",
       "2424 2008-07-01  27.64   723.45  0.000000\n",
       "2423 2008-07-02  27.54   763.25  0.000000\n",
       "2422 2008-07-03  26.85   740.35  0.000000\n",
       "2421 2008-07-07  26.59   732.85  0.000000\n",
       "2420 2008-07-08  26.12   736.65  0.000000\n",
       "2419 2008-07-09  26.09   746.20  0.000000\n",
       "2418 2008-07-10  26.79   731.70  0.000000\n",
       "2417 2008-07-11  33.32   712.30  0.000000\n",
       "2416 2008-07-14  31.09   736.50  0.000000\n",
       "2415 2008-07-15  30.40   742.10  0.000000\n",
       "...         ...    ...      ...       ...\n",
       "29   2018-01-05  11.26  1320.47  6.696179\n",
       "28   2018-01-08  11.19  1312.78  5.959741\n",
       "27   2018-01-09  10.79  1316.92  5.988792\n",
       "26   2018-01-10  10.79  1322.37  6.180513\n",
       "25   2018-01-11  10.96  1337.95  6.580116\n",
       "24   2018-01-12  11.62  1340.06  6.850995\n",
       "23   2018-01-16  12.09  1338.43  7.310829\n",
       "22   2018-01-17  11.77  1327.15  7.209422\n",
       "21   2018-01-18  12.26  1327.12  7.706528\n",
       "20   2018-01-19  11.43  1331.85  6.083269\n",
       "19   2018-01-22  11.66  1333.62  6.385480\n",
       "18   2018-01-23  11.72  1341.18  5.592633\n",
       "17   2018-01-24  13.38  1358.47  5.854043\n",
       "16   2018-01-25  13.04  1348.01  5.678251\n",
       "15   2018-01-26  12.98  1349.70  5.728235\n",
       "14   2018-01-29  13.25  1340.31  5.513741\n",
       "13   2018-01-30  13.86  1338.51  5.851900\n",
       "12   2018-01-31  12.97  1345.15  4.845238\n",
       "11   2018-02-01  12.32  1348.70  5.053575\n",
       "10   2018-02-02  13.11  1332.90  5.244418\n",
       "9    2018-02-05  14.35  1339.68  5.458411\n",
       "8    2018-02-06  13.80  1324.10  5.159011\n",
       "7    2018-02-07  13.62  1318.52  5.278265\n",
       "6    2018-02-08  14.85  1318.77  5.465651\n",
       "5    2018-02-09  14.93  1316.15  5.479442\n",
       "4    2018-02-12  14.37  1322.76  5.783904\n",
       "3    2018-02-13  14.07  1329.63  5.679579\n",
       "2    2018-02-14  14.97  1350.67  5.756023\n",
       "1    2018-02-15  15.03  1353.70  6.127875\n",
       "0    2018-02-16  13.96  1347.10  4.716945\n",
       "\n",
       "[2445 rows x 4 columns]"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_reg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "print('dataset = %1.0f' %row)\n",
    "\n",
    "for ele in rez:\n",
    "    print(ele,' = %8.4f'  %rez[ele].value)\n",
    "x = Pdict.loc[:,'vol'].values.reshape(len(Pdict),1)\n",
    "y = df_reg['']\n",
    "\n",
    "x2 = sm.add_constant(x)\n",
    "est = sm.OLS(y, x2)\n",
    "est2 = est.fit()\n",
    "print(est2.summary())\n",
    "# print(\"MODEL MSE\",est2.mse_model)\n",
    "print(\"MODEL MSE\",est2.mse_resid)\n",
    "print(\"MODEL TSE\",est2.mse_total)"
   ]
  }
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