code: def test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiVariate_refit_int_interval_yes_exog_yes_remainder_with_mocked():
      """
      Test output of backtesting_forecaster_multiseries in ForecasterAutoregMultiVariate
      with refit int, interval, gap, with mocked using exog and intervals
      (mocked done in Skforecast v0.9.0).
      """
      forecaster = ForecasterAutoregMultiVariate(
          regressor=Ridge(random_state=123),
          level="l1",
          lags=2,
          steps=2,
          transformer_series=None,
      )
  
      refit = 2
      n_validation = 20
      steps = 2
  
      (
          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=0,
          allow_incomplete_fold=False,
          refit=refit,
          fixed_train_size=True,
          exog=series["l1"].rename("exog_1"),
          interval=[5, 95],
          n_boot=100,
          random_state=123,
          in_sample_residuals=True,
          verbose=False,
      )
  
      expected_metric = pd.DataFrame(
          {
              "levels": ["l1"],
              "mean_absolute_error": [0.09237017311770493],
          }
      )
      expected_predictions = pd.DataFrame(
          data=np.array(
              [
                  [0.2983264, 0.14814112, 0.52611729],
                  [0.45367569, 0.3061465, 0.56042116],
                  [0.4802857, 0.33010042, 0.70807659],
                  [0.48384823, 0.33631904, 0.59059371],
                  [0.44991269, 0.27452568, 0.6567239],
                  [0.38062305, 0.20946396, 0.50828437],
                  [0.42817363, 0.25278662, 0.63498485],
                  [0.68209515, 0.51093605, 0.80975646],
                  [0.72786565, 0.58843297, 0.8652939],
                  [0.45147711, 0.32772617, 0.57845425],
                  [0.52904599, 0.38961331, 0.66647424],
                  [0.28657426, 0.16282332, 0.4135514],
                  [0.36296117, 0.24577117, 0.52321437],
                  [0.46902166, 0.37455162, 0.62846802],
                  [0.68519422, 0.56800422, 0.84544742],
                  [0.35197602, 0.25750597, 0.51142238],
                  [0.47338638, 0.29477692, 0.61652158],
                  [0.74059646, 0.6075235, 0.88275308],
                  [0.55112717, 0.37251772, 0.69426237],
                  [0.55778417, 0.4247112, 0.69994079],
              ]
          ),
          columns=["l1", "lower_bound", "upper_bound"],
          index=pd.RangeIndex(start=30, 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 30 for calling a global function with example usage: test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiVariate_refit_int_interval_yes_exog_yes_remainder_with_mocked() without return types