code: def test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiSeries_not_refit_exog_interval_with_mocked(
      forecaster,
  ):
      """
      Test output of backtesting_forecaster_multiseries in ForecasterAutoregMultiSeries
      and ForecasterAutoregMultiSeriesCustom without refit with mocked using exog
      and intervals (mocked done in Skforecast v0.5.0).
      """
  
      steps = 3
      n_validation = 12
  
      (
          metrics_levels,
          backtest_predictions,
      ) = backtesting_forecaster_multiseries(
          forecaster=forecaster,
          series=series,
          steps=steps,
          levels=["l1"],
          metric="mean_absolute_error",
          initial_train_size=len(series) - n_validation,
          refit=False,
          fixed_train_size=False,
          exog=series["l1"].rename("exog_1"),
          interval=[5, 95],
          n_boot=500,
          random_state=123,
          in_sample_residuals=True,
          verbose=False,
      )
  
      expected_metric = pd.DataFrame(
          {
              "levels": ["l1"],
              "mean_absolute_error": [0.14238176570382063],
          }
      )
      expected_predictions = pd.DataFrame(
          data=np.array(
              [
                  [0.64371728, 0.36845896, 0.91248693],
                  [0.47208179, 0.19871058, 0.74002421],
                  [0.52132498, 0.24592578, 0.78440458],
                  [0.3685079, 0.09324957, 0.63727755],
                  [0.42192697, 0.14855575, 0.68986939],
                  [0.46785602, 0.19245683, 0.73093562],
                  [0.61543694, 0.34017861, 0.88420659],
                  [0.41627752, 0.14290631, 0.68421995],
                  [0.4765156, 0.20111641, 0.7395952],
                  [0.65858347, 0.38332514, 0.92735312],
                  [0.49986428, 0.22649307, 0.7678067],
                  [0.51750994, 0.24211075, 0.78058954],
              ]
          ),
          columns=["l1", "l1_lower_bound", "l1_upper_bound"],
          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 10 for calling a global function with example usage: test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiSeries_not_refit_exog_interval_with_mocked(forecaster) without return types