code: def test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiSeries_not_refit_not_initial_train_size_with_mocked(
      forecaster,
  ):
      """
      Test output of backtesting_forecaster_multiseries in ForecasterAutoregMultiSeries
      and ForecasterAutoregMultiSeriesCustom without refit and initial_train_size
      is None with mocked, forecaster must be fitted, (mocked done in Skforecast v0.5.0).
      """
  
      forecaster.fit(series=series)
  
      steps = 1
      initial_train_size = None
  
      (
          metrics_levels,
          backtest_predictions,
      ) = backtesting_forecaster_multiseries(
          forecaster=forecaster,
          series=series,
          steps=steps,
          levels="l1",
          metric=mean_absolute_error,
          initial_train_size=initial_train_size,
          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(
          {
              "levels": ["l1"],
              "mean_absolute_error": [0.18616882305307128],
          }
      )
      expected_predictions = pd.DataFrame(
          {
              "l1": np.array(
                  [
                      0.48459053,
                      0.49259742,
                      0.51314434,
                      0.51387387,
                      0.49192289,
                      0.53266761,
                      0.49986433,
                      0.496257,
                      0.49677997,
                      0.49641078,
                      0.52024409,
                      0.49255581,
                      0.47860725,
                      0.50888892,
                      0.51923275,
                      0.4773962,
                      0.49249923,
                      0.51342903,
                      0.50350073,
                      0.50946515,
                      0.51912045,
                      0.50583902,
                      0.50272475,
                      0.51237963,
                      0.48600893,
                      0.49942566,
                      0.49056705,
                      0.49810661,
                      0.51591527,
                      0.47512221,
                      0.51005943,
                      0.5003548,
                      0.50409177,
                      0.49838669,
                      0.49366925,
                      0.50348344,
                      0.52748975,
                      0.51740335,
                      0.49023212,
                      0.50969436,
                      0.47668736,
                      0.50262471,
                      0.50267211,
                      0.52623492,
                      0.47776998,
                      0.50850968,
                      0.53127329,
                      0.49010354,
                  ]
              )
          },
          index=pd.RangeIndex(start=2, 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 4 for calling a global function with example usage: test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiSeries_not_refit_not_initial_train_size_with_mocked(forecaster) without return types