diff --git a/test/integration/models/test_custom_model_introduction.py b/test/integration/models/test_custom_model_introduction.py
index c5514f2b5b..a7be5c2c77 100644
--- a/test/integration/models/test_custom_model_introduction.py
+++ b/test/integration/models/test_custom_model_introduction.py
@@ -147,7 +147,7 @@ def get_simple_pipeline(multi_data):
             exog_list.append(PipelineNode(data_id))
         if 'hist_' in data_id:
             lagged_node = PipelineNode('lagged', nodes_from=[PipelineNode(data_id)])
-            lagged_node.parameters = {'window_size': 1}
+            lagged_node.parameters = {'window_size': 2}
 
             hist_list.append(lagged_node)
 
diff --git a/test/integration/pipelines/tuning/test_pipeline_tuning.py b/test/integration/pipelines/tuning/test_pipeline_tuning.py
index 34cdb062ab..60116d7098 100644
--- a/test/integration/pipelines/tuning/test_pipeline_tuning.py
+++ b/test/integration/pipelines/tuning/test_pipeline_tuning.py
@@ -2,6 +2,8 @@
 from time import time
 
 import pytest
+
+from fedot.core.repository.dataset_types import DataTypesEnum
 from golem.core.tuning.hyperopt_tuner import get_node_parameters_for_hyperopt
 from golem.core.tuning.iopt_tuner import IOptTuner
 from golem.core.tuning.optuna_tuner import OptunaTuner
@@ -216,6 +218,20 @@ def run_pipeline_tuner(train_data,
                        cv=None,
                        iterations=3,
                        early_stopping_rounds=None, **kwargs):
+
+    if train_data.data_type in (DataTypesEnum.ts, DataTypesEnum.multi_ts):
+        forecast_length = train_data.task.task_params.forecast_length
+        folds = cv or 1
+        validation_blocks = 1
+        max_window = int(train_data.features.shape[0] / (folds + 1)) - (forecast_length * validation_blocks) - 1
+        ssp = {'window_size': {'hyperopt-dist': hp.uniformint, 'sampling-scope': [2, max_window], 'type': 'discrete'}}
+        if search_space.custom_search_space is None:
+            search_space.custom_search_space = {'lagged': ssp}
+        else:
+            search_space.custom_search_space['lagged'] = ssp
+        search_space.replace_default_search_space = True
+        search_space.parameters_per_operation = search_space.get_parameters_dict()
+
     # Pipeline tuning
     pipeline_tuner = TunerBuilder(train_data.task) \
         .with_tuner(tuner) \
diff --git a/test/integration/real_applications/test_examples.py b/test/integration/real_applications/test_examples.py
index dfb0a7d75e..bb9e6b2cb4 100644
--- a/test/integration/real_applications/test_examples.py
+++ b/test/integration/real_applications/test_examples.py
@@ -1,3 +1,5 @@
+import os
+
 from datetime import timedelta
 
 import numpy as np
@@ -45,8 +47,10 @@ def test_gapfilling_example():
 
 def test_exogenous_ts_example():
     path = fedot_project_root().joinpath('test/data/simple_sea_level.csv')
+    test = os.environ.pop('PYTEST_CURRENT_TEST')
     run_exogenous_experiment(path_to_file=path,
                              len_forecast=50, with_exog=True)
+    os.environ['PYTEST_CURRENT_TEST'] = test
 
 
 def test_nemo_multiple_points_example():
@@ -84,7 +88,9 @@ def test_api_example():
     prediction = run_classification_example(timeout=1, with_tuning=with_tuning)
     assert prediction is not None
 
+    test = os.environ.pop('PYTEST_CURRENT_TEST')
     forecast = run_ts_forecasting_example(dataset='australia', timeout=2, with_tuning=with_tuning)
+    os.environ['PYTEST_CURRENT_TEST'] = test
     assert forecast is not None
 
     pareto = run_classification_multiobj_example(timeout=1, with_tuning=with_tuning)
diff --git a/test/integration/real_applications/test_model_result_reproducing.py b/test/integration/real_applications/test_model_result_reproducing.py
index 7e4f58ad6b..03082438e7 100644
--- a/test/integration/real_applications/test_model_result_reproducing.py
+++ b/test/integration/real_applications/test_model_result_reproducing.py
@@ -31,7 +31,8 @@ def get_fitted_fedot(forecast_length, train_data, **kwargs):
               'seed': 1,
               'timeout': None,
               'pop_size': 50,
-              'num_of_generations': 5}
+              'num_of_generations': 5,
+              'with_tuning': False}
     params.update(kwargs)
     fedot = Fedot(**params)
     fedot.fit(train_data)
diff --git a/test/integration/utilities/test_pipeline_import_export.py b/test/integration/utilities/test_pipeline_import_export.py
index 1fa7fae267..2db2652a8c 100644
--- a/test/integration/utilities/test_pipeline_import_export.py
+++ b/test/integration/utilities/test_pipeline_import_export.py
@@ -346,7 +346,7 @@ def test_export_without_path_correctly():
 
 
 def test_data_model_types_forecasting_pipeline_fit():
-    train_data, test_data = get_ts_data(forecast_length=10)
+    train_data, test_data = get_ts_data(n_steps = 200, forecast_length=10)
 
     pipeline = get_multiscale_pipeline()
     pipeline.fit(train_data)