code: def test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiVariate_no_refit_exog_interval_gap_with_mocked():
      """
      Test output of backtesting_forecaster_multiseries in ForecasterAutoregMultiVariate
      with no refit and gap with mocked using exog and intervals
      (mocked done in Skforecast v0.5.0).
      """
      forecaster = ForecasterAutoregMultiVariate(
          regressor=Ridge(random_state=123),
          level="l1",
          lags=2,
          steps=8,
          transformer_series=None,
      )
  
      n_validation = 20
      steps = 5
      gap = 3
  
      (
          metrics_levels,
          backtest_predictions,
      ) = backtesting_forecaster_multiseries(
          forecaster=forecaster,
          series=series,
          steps=steps,
          levels="l1",
          metric="mean_absolute_error",
          initial_train_size=len(series) - n_validation,
          gap=gap,
          allow_incomplete_fold=True,
          refit=False,
          fixed_train_size=False,
          exog=series["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": [0.10867753185751189],
          }
      )
      expected_predictions = pd.DataFrame(
          data=np.array(
              [
                  [0.5137416, 0.28565005, 0.64960534],
                  [0.51578881, 0.36235612, 0.71123006],
                  [0.38569703, 0.20965762, 0.51379331],
                  [0.41784889, 0.23241384, 0.58140101],
                  [0.69352545, 0.51075098, 0.88011232],
                  [0.7137808, 0.48568926, 0.84964454],
                  [0.52155299, 0.3681203, 0.71699424],
                  [0.51871169, 0.34267227, 0.64680796],
                  [0.31342947, 0.12799441, 0.47698158],
                  [0.4337246, 0.25095013, 0.62031147],
                  [0.44486807, 0.21677652, 0.58073181],
                  [0.67773806, 0.52430536, 0.87317931],
                  [0.3732339, 0.19719449, 0.50133018],
                  [0.44959589, 0.26416083, 0.613148],
                  [0.69181652, 0.50904205, 0.87840338],
                  [0.51679906, 0.28870751, 0.6526628],
                  [0.49803962, 0.34460692, 0.69348087],
              ]
          ),
          columns=["l1", "lower_bound", "upper_bound"],
          index=pd.RangeIndex(start=33, stop=50, step=1),
      )
  
      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 27 for calling a global function with example usage: test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiVariate_no_refit_exog_interval_gap_with_mocked() without return types