code: def test_historical_forecasts_future_cov_local_models(self):
      model = AutoARIMA()
      assert model.min_train_series_length == 10
      series = tg.sine_timeseries(length=11)
      res = model.historical_forecasts(
          series,
          future_covariates=series,
          retrain=True,
          forecast_horizon=1,
      )
      # AutoARIMA has a minimum train length of 10, with horizon=1, we expect one forecast at last point
      # (series has length 11)
      assert len(res) == 1
      assert series.end_time() == res.time_index[0]
  
      model.fit(series, future_covariates=series)
      with pytest.raises(ValueError) as msg:
          model.historical_forecasts(
              series,
              future_covariates=series,
              retrain=False,
              forecast_horizon=1,
          )
      assert str(msg.value).startswith(
          "FutureCovariatesLocalForecastingModel does not support historical forecasting "
          "with `retrain` set to `False`"
      )
  
      # passing non-supported covariates
      with pytest.raises(ValueError) as msg:
          model.historical_forecasts(
              series,
              past_covariates=series,
              retrain=True,
          )
      assert str(msg.value).startswith(
          "Model cannot be fit/trained with `past_covariates`."
      )
  
imports: import itertools
  from itertools import product
  import numpy
  import pandas
  import pytest
  import darts
  from darts import TimeSeries, concatenate
  from darts.dataprocessing.transformers import Scaler
  from darts.datasets import AirPassengersDataset
  from darts.logging import get_logger
  from darts.models import ARIMA, AutoARIMA, CatBoostModel, LightGBMModel, LinearRegressionModel, NaiveSeasonal, NotImportedModule
  from darts.tests.conftest import tfm_kwargs
  from darts.utils import timeseries_generation
label_desc: Use image node_id 3 for calling the TestHistoricalforecast obj's underlying member method code with example usage: obj.test_historical_forecasts_future_cov_local_models() without return types