code: def test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiSeries_refit_int_interval_yes_exog_not_allow_remainder_gap_with_mocked(
      forecaster,
  ):
      """
      Test output of backtesting_forecaster_multiseries in ForecasterAutoregMultiSeries
      and ForecasterAutoregMultiSeriesCustom with refit int, interval, gap,
      with mocked using exog and intervals (mocked done in Skforecast v0.9.0).
      """
      series_with_index = series.copy()
      series_with_index.index = pd.date_range(
          start="2022-01-01", periods=50, freq="D"
      )
      exog_with_index = series["l1"].rename("exog_1").copy()
      exog_with_index.index = pd.date_range(
          start="2022-01-01", periods=50, freq="D"
      )
  
      refit = 3
      n_validation = 20
      steps = 4
      gap = 3
  
      (
          metrics_levels,
          backtest_predictions,
      ) = backtesting_forecaster_multiseries(
          forecaster=forecaster,
          series=series_with_index,
          steps=steps,
          levels=["l2"],
          metric="mean_absolute_error",
          initial_train_size=len(series_with_index) - n_validation,
          gap=gap,
          allow_incomplete_fold=False,
          refit=refit,
          fixed_train_size=False,
          exog=exog_with_index,
          interval=[5, 95],
          n_boot=100,
          random_state=123,
          in_sample_residuals=True,
          verbose=False,
      )
  
      expected_metric = pd.DataFrame(
          {
              "levels": ["l2"],
              "mean_absolute_error": [0.2791832310123065],
          }
      )
      expected_predictions = pd.DataFrame(
          data=np.array(
              [
                  [0.49984026, 0.00509982, 0.82464616],
                  [0.4767447, -0.0798953, 0.80487146],
                  [0.43791384, -0.12045877, 0.81344287],
                  [0.47690063, -0.01831127, 0.85480226],
                  [0.63619086, 0.14145042, 0.96099675],
                  [0.65328344, 0.09664345, 0.98141021],
                  [0.50150406, -0.05686855, 0.8770331],
                  [0.54283634, 0.04762444, 0.92073797],
                  [0.37097633, -0.1237641, 0.69578223],
                  [0.43922059, -0.11741941, 0.76734736],
                  [0.47379722, -0.08457539, 0.84932626],
                  [0.62696782, 0.13175592, 1.00486945],
                  [0.45263688, -0.09848725, 0.84471127],
                  [0.5005012, -0.02743982, 0.95029956],
                  [0.66342359, 0.10579924, 1.20771224],
                  [0.53547991, 0.02357046, 0.89862351],
              ]
          ),
          columns=["l2", "l2_lower_bound", "l2_upper_bound"],
          index=pd.date_range(start="2022-02-03", periods=16, 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 19 for calling a global function with example usage: test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiSeries_refit_int_interval_yes_exog_not_allow_remainder_gap_with_mocked(forecaster) without return types