code: def test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiVariate_refit_exog_interval_gap_with_mocked():
      """
      Test output of backtesting_forecaster_multiseries in ForecasterAutoregMultiVariate
      with refit, gap, allow_incomplete_fold False 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=False,
          refit=True,
          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": [0.09906557188440204],
          }
      )
      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],
                  [0.73709708, 0.60256116, 0.87889663],
                  [0.49379408, 0.34235281, 0.70108827],
                  [0.54129634, 0.38342955, 0.66423569],
                  [0.2889167, 0.13545924, 0.45541277],
                  [0.41762991, 0.26652975, 0.58517659],
                  [0.4281944, 0.26680135, 0.56842703],
                  [0.6800295, 0.53425961, 0.86349246],
                  [0.3198172, 0.18545173, 0.44111693],
                  [0.45269985, 0.29948117, 0.57043644],
                  [0.76214215, 0.63320969, 0.90810797],
              ]
          ),
          columns=["l1", "lower_bound", "upper_bound"],
          index=pd.RangeIndex(start=33, stop=48, 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 28 for calling a global function with example usage: test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiVariate_refit_exog_interval_gap_with_mocked() without return types