code: def test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiSeries_no_refit_different_lengths_with_mocked(
      forecaster,
  ):
      """
      Test output of backtesting_forecaster_multiseries in ForecasterAutoregMultiSeries
      and ForecasterAutoregMultiSeriesCustom with no refit and gap with
      mocked using exog and intervals and series with different lengths
      (mocked done in Skforecast v0.5.0).
      """
      n_validation = 20
      steps = 5
      gap = 3
  
      (
          metrics_levels,
          backtest_predictions,
      ) = backtesting_forecaster_multiseries(
          forecaster=forecaster,
          series=series_with_nans,
          steps=steps,
          levels="l1",
          metric="mean_absolute_error",
          initial_train_size=len(series_with_nans) - n_validation,
          gap=gap,
          allow_incomplete_fold=True,
          refit=False,
          fixed_train_size=False,
          exog=series_with_nans["l1"].rename("exog_1"),
          interval=[5, 95],
          n_boot=150,
          random_state=123,
          in_sample_residuals=True,
          verbose=False,
      )
  
      expected_metric = pd.DataFrame(
          {
              "levels": ["l1"],
              "mean_absolute_error": [0.11243765852459384],
          }
      )
      expected_predictions = pd.DataFrame(
          data=np.array(
              [
                  [0.49746847, 0.24620019, 0.74208308],
                  [0.46715961, 0.27280913, 0.69897019],
                  [0.42170236, 0.21384761, 0.6338432],
                  [0.47242371, 0.23550111, 0.68264162],
                  [0.66450589, 0.4128072, 0.87549193],
                  [0.67311291, 0.42184464, 0.91772752],
                  [0.48788629, 0.29353581, 0.71969688],
                  [0.55141437, 0.34355962, 0.76355521],
                  [0.33369285, 0.09677024, 0.54391075],
                  [0.43287852, 0.18117983, 0.64386456],
                  [0.46643379, 0.21516552, 0.7110484],
                  [0.6535986, 0.45924812, 0.88540919],
                  [0.38328273, 0.17542798, 0.59542356],
                  [0.49931045, 0.26238785, 0.70952835],
                  [0.70119564, 0.44949695, 0.91218168],
                  [0.49290276, 0.24163448, 0.73751736],
                  [0.54653561, 0.35218513, 0.7783462],
              ]
          ),
          columns=["l1", "l1_lower_bound", "l1_upper_bound"],
          index=pd.RangeIndex(start=33, 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 15 for calling a global function with example usage: test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiSeries_no_refit_different_lengths_with_mocked(forecaster) without return types