code: def test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiSeries_no_refit_levels_metrics_remainder_with_mocked(
      forecaster,
  ):
      """
      Test output of backtesting_forecaster_multiseries in ForecasterAutoregMultiSeries
      and ForecasterAutoregMultiSeriesCustom with no refit, remainder, multiple
      levels and metrics with mocked (mocked done in Skforecast v0.5.0).
      """
  
      steps = 5
      n_validation = 12
  
      (
          metrics_levels,
          backtest_predictions,
      ) = backtesting_forecaster_multiseries(
          forecaster=forecaster,
          series=series,
          steps=steps,
          levels=None,
          metric=["mean_absolute_error", mean_absolute_error],
          initial_train_size=len(series) - n_validation,
          refit=False,
          fixed_train_size=False,
          exog=None,
          interval=None,
          n_boot=500,
          random_state=123,
          in_sample_residuals=True,
          verbose=False,
      )
  
      expected_metric = pd.DataFrame(
          data=[
              ["l1", 0.21143995953996186, 0.21143995953996186],
              ["l2", 0.2194174144550234, 0.2194174144550234],
          ],
          columns=[
              "levels",
              "mean_absolute_error",
              "mean_absolute_error",
          ],
      )
      expected_predictions = pd.DataFrame(
          {
              "l1": np.array(
                  [
                      0.4978839,
                      0.46288427,
                      0.48433446,
                      0.48677605,
                      0.48562473,
                      0.50259242,
                      0.49536197,
                      0.48478881,
                      0.48496106,
                      0.48555902,
                      0.49673897,
                      0.4576795,
                  ]
              ),
              "l2": np.array(
                  [
                      0.50266337,
                      0.53045945,
                      0.50527774,
                      0.50315834,
                      0.50452649,
                      0.47372756,
                      0.51226827,
                      0.50650107,
                      0.50420766,
                      0.50448097,
                      0.52211914,
                      0.51092531,
                  ]
              ),
          },
          index=pd.RangeIndex(start=38, 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 8 for calling a global function with example usage: test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiSeries_no_refit_levels_metrics_remainder_with_mocked(forecaster) without return types