code: def test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiVariate_not_refit_not_initial_train_size_with_mocked():
      """
      Test output of backtesting_forecaster_multiseries in ForecasterAutoregMultiVariate
      without refit and initial_train_size is None with mocked, forecaster must be fitted,
      (mocked done in Skforecast v0.6.0).
      """
  
      forecaster = ForecasterAutoregMultiVariate(
          regressor=Ridge(random_state=123),
          level="l1",
          lags=2,
          steps=3,
          transformer_series=None,
      )
      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": [0.17959810844511925],
          }
      )
      expected_predictions = pd.DataFrame(
          {
              "l1": np.array(
                  [
                      0.42102839,
                      0.47138953,
                      0.52252844,
                      0.54594276,
                      0.51253167,
                      0.57557448,
                      0.45455673,
                      0.42240387,
                      0.48555804,
                      0.46974027,
                      0.52264755,
                      0.45674877,
                      0.43440543,
                      0.47187135,
                      0.59653789,
                      0.41804686,
                      0.53408781,
                      0.58853203,
                      0.49880785,
                      0.57834799,
                      0.47345798,
                      0.46890693,
                      0.45765737,
                      0.59034503,
                      0.46198262,
                      0.49384858,
                      0.54212837,
                      0.56867955,
                      0.5095804,
                      0.47751184,
                      0.50402253,
                      0.48993588,
                      0.52583999,
                      0.4306855,
                      0.42782129,
                      0.52841356,
                      0.62570147,
                      0.55585762,
                      0.48719966,
                      0.48508799,
                      0.37122115,
                      0.53115279,
                      0.47119561,
                      0.52734455,
                      0.41557646,
                      0.57546277,
                      0.57700474,
                      0.50898628,
                  ]
              )
          },
          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 21 for calling a global function with example usage: test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiVariate_not_refit_not_initial_train_size_with_mocked() without return types