code: def test_exogenous_variables_support(self, model):
      # test case with pd.DatetimeIndex
      target_dt_idx = self.ts_gaussian
      fc_dt_idx = self.ts_gaussian_long
  
      # test case with numerical pd.RangeIndex
      target_num_idx = TimeSeries.from_times_and_values(
          times=tg.generate_index(
              start=0, length=len(self.ts_gaussian)
          ),
          values=self.ts_gaussian.all_values(copy=False),
      )
      fc_num_idx = TimeSeries.from_times_and_values(
          times=tg.generate_index(
              start=0, length=len(self.ts_gaussian_long)
          ),
          values=self.ts_gaussian_long.all_values(copy=False),
      )
  
      for target, future_covariates in zip(
          [target_dt_idx, target_num_idx], [fc_dt_idx, fc_num_idx]
      ):
          if isinstance(target.time_index, pd.RangeIndex):
              try:
                  # _supports_range_index raises a ValueError if model does not support RangeIndex
                  model._supports_range_index
              except ValueError:
                  continue
  
          # Test models runnability - proper future covariates slicing
          model.fit(target, future_covariates=future_covariates)
          prediction = model.predict(
              self.forecasting_horizon,
              future_covariates=future_covariates,
          )
  
          assert len(prediction) == self.forecasting_horizon
  
          # Test mismatch in length between exogenous variables and forecasting horizon
          with pytest.raises(ValueError):
              model.predict(
                  self.forecasting_horizon,
                  future_covariates=tg.gaussian_timeseries(
                      start=future_covariates.start_time(),
                      length=self.forecasting_horizon - 1,
                  ),
              )
  
          # Test mismatch in time-index/length between series and exogenous variables
          with pytest.raises(ValueError):
              model.fit(target, future_covariates=target[:-1])
          with pytest.raises(ValueError):
              model.fit(target[1:], future_covariates=target[:-1])
  
imports: import copy
  import itertools
  import os
  import pathlib
  from typing import Callable
  from unittest.mock import Mock, patch
  import numpy
  import pandas
  import pytest
  from darts.datasets import AirPassengersDataset, IceCreamHeaterDataset
  from darts.logging import get_logger
  from darts.metrics import mape
  from darts.models import ARIMA, BATS, FFT, TBATS, VARIMA, AutoARIMA, Croston, ExponentialSmoothing, FourTheta, KalmanForecaster, LinearRegressionModel, NaiveDrift, NaiveMean, NaiveMovingAverage, NaiveSeasonal, NotImportedModule, Prophet, RandomForest, RegressionModel, StatsForecastAutoARIMA, StatsForecastAutoCES, StatsForecastAutoETS, StatsForecastAutoTheta, Theta
  from darts.models.forecasting.forecasting_model import LocalForecastingModel, TransferableFutureCovariatesLocalForecastingModel
  from darts.timeseries import TimeSeries
  from darts.utils import timeseries_generation
  from darts.utils.utils import ModelMode, SeasonalityMode, TrendMode
label_desc: Use image node_id 9 for calling the TestLocalForecastingModels obj's underlying member method code with example usage: obj.test_exogenous_variables_support(model) without return types