code: def test_output_random_search_forecaster_ForecasterAutoreg_with_mocked():
      """
      Test output of random_search_forecaster in ForecasterAutoreg with mocked
      (mocked done in Skforecast v0.4.3)
      """
      forecaster = ForecasterAutoreg(
          regressor=Ridge(random_state=123),
          lags=2,  # Placeholder, the value will be overwritten
      )
  
      steps = 3
      n_validation = 12
      y_train = y[:-n_validation]
      lags_grid = [2, 4]
      param_distributions = {"alpha": np.logspace(-5, 3, 10)}
      n_iter = 3
  
      results = random_search_forecaster(
          forecaster=forecaster,
          y=y,
          lags_grid=lags_grid,
          param_distributions=param_distributions,
          steps=steps,
          refit=False,
          metric="mean_squared_error",
          initial_train_size=len(y_train),
          fixed_train_size=False,
          n_iter=n_iter,
          random_state=123,
          return_best=False,
          verbose=False,
      )
  
      expected_results = pd.DataFrame(
          {
              "lags": [
                  [1, 2],
                  [1, 2],
                  [1, 2, 3, 4],
                  [1, 2, 3, 4],
                  [1, 2, 3, 4],
                  [1, 2],
              ],
              "params": [
                  {"alpha": 1e-05},
                  {"alpha": 0.03593813663804626},
                  {"alpha": 1e-05},
                  {"alpha": 0.03593813663804626},
                  {"alpha": 16.681005372000556},
                  {"alpha": 16.681005372000556},
              ],
              "mean_squared_error": np.array(
                  [
                      0.06460234,
                      0.06475887,
                      0.06776596,
                      0.06786132,
                      0.0713478,
                      0.07161,
                  ]
              ),
              "alpha": np.array(
                  [
                      1.00000000e-05,
                      3.59381366e-02,
                      1.00000000e-05,
                      3.59381366e-02,
                      1.66810054e01,
                      1.66810054e01,
                  ]
              ),
          },
          index=pd.Index([1, 0, 4, 3, 5, 2], dtype="int64"),
      )
  
      pd.testing.assert_frame_equal(results, expected_results)
  
file_path: skforecast/skforecast/model_selection/tests/test_random_search_forecaster.py
imports: import numpy
  import pandas
  from sklearn.metrics import mean_squared_error
  from sklearn.linear_model import Ridge
  from skforecast.ForecasterAutoreg import ForecasterAutoreg
  from skforecast.model_selection import random_search_forecaster
  from tqdm import tqdm
  from functools import partialmethod
  from .fixtures_model_selection import y
label_desc: Use image node_id 1 for calling a global function with example usage: test_output_random_search_forecaster_ForecasterAutoreg_with_mocked() without return types