code: def test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiSeries_refit_fixed_train_size_exog_interval_with_mocked(
      forecaster,
  ):
      """
      Test output of backtesting_forecaster_multiseries in ForecasterAutoregMultiSeries
      and ForecasterAutoregMultiSeriesCustom with refit and fixed_train_size 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=True,
          fixed_train_size=True,
          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": [0.1509587543248219],
          }
      )
      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],
                  [0.38179014, 0.15353798, 0.65675721],
                  [0.43343713, 0.19888319, 0.70802106],
                  [0.4695322, 0.18716947, 0.74043601],
                  [0.57891069, 0.31913315, 0.84636925],
                  [0.41212578, 0.15090397, 0.69394422],
                  [0.46851038, 0.20736343, 0.76349422],
                  [0.63190066, 0.35803673, 0.90303047],
                  [0.49132695, 0.21857874, 0.78112082],
                  [0.51665452, 0.26139311, 0.80879351],
              ]
          ),
          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 11 for calling a global function with example usage: test_output_backtesting_forecaster_multiseries_ForecasterAutoregMultiSeries_refit_fixed_train_size_exog_interval_with_mocked(forecaster) without return types