code: def test_output_random_search_forecaster_multiseries_ForecasterAutoregMultiVariate_with_mocked():
      """
      Test output of random_search_forecaster_multiseries in ForecasterAutoregMultiVariate
      with mocked (mocked done in Skforecast v0.6.0)
      """
      forecaster = ForecasterAutoregMultiVariate(
          regressor=Ridge(random_state=123),
          level="l1",
          lags=2,
          steps=3,
          transformer_series=None,
      )
  
      steps = 3
      n_validation = 12
      lags_grid = [2, 4]
      param_distributions = {"alpha": np.logspace(-5, 3, 10)}
      n_iter = 3
  
      results = random_search_forecaster_multivariate(
          forecaster=forecaster,
          series=series,
          param_distributions=param_distributions,
          steps=steps,
          metric="mean_absolute_error",
          initial_train_size=len(series) - n_validation,
          fixed_train_size=False,
          levels=None,
          exog=None,
          lags_grid=lags_grid,
          refit=False,
          n_iter=n_iter,
          return_best=False,
          verbose=True,
      )
  
      expected_results = pd.DataFrame(
          {
              "levels": [
                  ["l1"],
                  ["l1"],
                  ["l1"],
                  ["l1"],
                  ["l1"],
                  ["l1"],
              ],
              "lags": [
                  [1, 2],
                  [1, 2],
                  [1, 2],
                  [1, 2, 3, 4],
                  [1, 2, 3, 4],
                  [1, 2, 3, 4],
              ],
              "params": [
                  {"alpha": 1e-05},
                  {"alpha": 0.03593813663804626},
                  {"alpha": 16.681005372000556},
                  {"alpha": 16.681005372000556},
                  {"alpha": 0.03593813663804626},
                  {"alpha": 1e-05},
              ],
              "mean_absolute_error": np.array(
                  [
                      0.20107097,
                      0.20135665,
                      0.20991177,
                      0.21121154,
                      0.22640335,
                      0.22645387,
                  ]
              ),
              "alpha": np.array(
                  [
                      1.00000000e-05,
                      3.59381366e-02,
                      1.66810054e01,
                      1.66810054e01,
                      3.59381366e-02,
                      1.00000000e-05,
                  ]
              ),
          },
          index=pd.Index([1, 0, 2, 5, 3, 4], dtype="int64"),
      )
  
      pd.testing.assert_frame_equal(results, expected_results)
  
file_path: skforecast/skforecast/model_selection_multiseries/tests/test_random_search_forecaster_multiseries.py
imports: import pytest
  import numpy
  import pandas
  from sklearn.linear_model import Ridge
  from skforecast.ForecasterAutoregMultiSeries import ForecasterAutoregMultiSeries
  from skforecast.ForecasterAutoregMultiSeriesCustom import ForecasterAutoregMultiSeriesCustom
  from skforecast.ForecasterAutoregMultiVariate import ForecasterAutoregMultiVariate
  from skforecast.model_selection_multiseries import random_search_forecaster_multiseries
  from skforecast.model_selection_multiseries import random_search_forecaster_multivariate
  from tqdm import tqdm
  from functools import partialmethod
  from .fixtures_model_selection_multiseries import series
label_desc: Use image node_id 4 for calling a global function with example usage: test_output_random_search_forecaster_multiseries_ForecasterAutoregMultiVariate_with_mocked() without return types