code: def test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiVariate_refit_fixed_train_size_exog_interval_gap_with_mocked():
      """
      Test output of backtesting_forecaster_multiseries in ForecasterAutoregMultiVariate
      with refit, fixed_train_size, gap, with mocked using exog and intervals
      (mocked done in Skforecast v0.5.0).
      """
      series_datetime = series.copy()
      series_datetime.index = pd.date_range(
          start="2022-01-01", periods=50, freq="D"
      )
  
      forecaster = ForecasterAutoregMultiVariate(
          regressor=Ridge(random_state=123),
          level="l1",
          lags=2,
          steps=10,
          transformer_series=None,
      )
  
      n_validation = 20
      steps = 5
      gap = 5
  
      (
          metrics_levels,
          backtest_predictions,
      ) = backtesting_forecaster_multiseries(
          forecaster=forecaster,
          series=series_datetime,
          steps=steps,
          levels="l1",
          metric="mean_absolute_error",
          initial_train_size=len(series_datetime) - n_validation,
          gap=gap,
          allow_incomplete_fold=False,
          refit=True,
          fixed_train_size=True,
          exog=series_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": [0.12073089072357064],
          }
      )
      expected_predictions = pd.DataFrame(
          data=np.array(
              [
                  [0.40010139, 0.21491844, 0.52790634],
                  [0.42717215, 0.23067944, 0.57988887],
                  [0.68150611, 0.48700348, 0.81952219],
                  [0.66167269, 0.46929506, 0.87762411],
                  [0.48946946, 0.36803878, 0.69919005],
                  [0.52955424, 0.36121274, 0.7342489],
                  [0.30621348, 0.11465701, 0.46702924],
                  [0.44140106, 0.27497225, 0.62523765],
                  [0.41294246, 0.26739719, 0.58273245],
                  [0.66798745, 0.51402456, 0.82567436],
                  [0.35206832, 0.19485472, 0.6001923],
                  [0.41828203, 0.28154037, 0.58081107],
                  [0.6605119, 0.44992937, 0.79751069],
                  [0.49225437, 0.31367508, 0.67624609],
                  [0.52528842, 0.33700505, 0.74482225],
              ]
          ),
          columns=["l1", "lower_bound", "upper_bound"],
          index=pd.date_range(start="2022-02-05", periods=15, freq="D"),
      )
      backtest_predictions = backtest_predictions.asfreq("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 29 for calling a global function with example usage: test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiVariate_refit_fixed_train_size_exog_interval_gap_with_mocked() without return types