code: def test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiSeries_refit_fixed_train_size_different_lengths_with_mocked(
      forecaster,
  ):
      """
      Test output of backtesting_forecaster_multiseries in ForecasterAutoregMultiSeries
      and ForecasterAutoregMultiSeriesCustom with refit, fixed_train_size, gap,
      with mocked using exog and intervals (mocked done in Skforecast v0.5.0).
      """
      series_with_nans_datetime = series_with_nans.copy()
      series_with_nans_datetime.index = pd.date_range(
          start="2022-01-01", periods=50, freq="D"
      )
  
      n_validation = 20
      steps = 5
      gap = 5
  
      (
          metrics_levels,
          backtest_predictions,
      ) = backtesting_forecaster_multiseries(
          forecaster=forecaster,
          series=series_with_nans_datetime,
          steps=steps,
          levels="l1",
          metric="mean_absolute_error",
          initial_train_size=len(series_with_nans_datetime)
          - n_validation,
          gap=gap,
          allow_incomplete_fold=False,
          refit=True,
          fixed_train_size=True,
          exog=series_with_nans_datetime["l1"].rename("exog_1"),
          interval=[5, 95],
          n_boot=150,
          random_state=123,
          in_sample_residuals=True,
          verbose=False,
      )
  
      expected_metric = pd.DataFrame(
          {
              "levels": ["l1"],
              "mean_absolute_error": [0.1355099897175138],
          }
      )
      expected_predictions = pd.DataFrame(
          data=np.array(
              [
                  [0.42170236, 0.21384761, 0.6338432],
                  [0.47242371, 0.23550111, 0.68264162],
                  [0.66450589, 0.4128072, 0.87549193],
                  [0.67311586, 0.46534536, 0.89662809],
                  [0.487886, 0.27487735, 0.65050566],
                  [0.52759202, 0.30254031, 0.7316064],
                  [0.33021382, 0.11679102, 0.52056867],
                  [0.4226274, 0.16874895, 0.61548288],
                  [0.44647715, 0.22033296, 0.65301466],
                  [0.61435678, 0.37793909, 0.81285962],
                  [0.41671844, 0.13568381, 0.67943385],
                  [0.47385345, 0.19025177, 0.76849597],
                  [0.62360146, 0.39888165, 0.85075261],
                  [0.49407875, 0.24011478, 0.78855477],
                  [0.51234652, 0.26828928, 0.81339595],
              ]
          ),
          columns=["l1", "l1_lower_bound", "l1_upper_bound"],
          index=pd.date_range(start="2022-02-05", periods=15, freq="D"),
      )
  
      pd.testing.assert_frame_equal(expected_metric, metrics_levels)
      pd.testing.assert_frame_equal(
          expected_predictions, backtest_predictions
      )
  
imports: import re
  import pytest
  import numpy
  import pandas
  from sklearn.linear_model import Ridge
  from sklearn.metrics import mean_absolute_error
  from skforecast.exceptions import IgnoredArgumentWarning
  from skforecast.ForecasterAutoreg import ForecasterAutoreg
  from skforecast.ForecasterAutoregMultiSeries import ForecasterAutoregMultiSeries
  from skforecast.ForecasterAutoregMultiSeriesCustom import ForecasterAutoregMultiSeriesCustom
  from skforecast.ForecasterAutoregMultiVariate import ForecasterAutoregMultiVariate
  from skforecast.model_selection_multiseries import backtesting_forecaster_multiseries
  from skforecast.model_selection_multiseries import backtesting_forecaster_multivariate
  from .fixtures_model_selection_multiseries import series
label_desc: Use image node_id 17 for calling a global function with example usage: test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiSeries_refit_fixed_train_size_different_lengths_with_mocked(forecaster) without return types