code: def test_dirrec_against_recursive_accumulated_error():
      """Test recursive and dirrec regressor strategies.
  
      dirrec regressor should produce lower error due to less cumulative error
      """
      y = load_airline()
      y_train, y_test = temporal_train_test_split(y, test_size=24)
      fh = ForecastingHorizon(y_test.index, is_relative=False)
  
      estimator = LinearRegression()
      recursive = make_reduction(
          estimator, scitype="tabular-regressor", strategy="recursive"
      )
      dirrec = make_reduction(
          estimator, scitype="tabular-regressor", strategy="dirrec"
      )
  
      preds_recursive = recursive.fit(y_train, fh=fh).predict(fh)
      preds_dirrec = dirrec.fit(y_train, fh=fh).predict(fh)
  
      assert mean_absolute_percentage_error(
          y_test, preds_dirrec
      ) < mean_absolute_percentage_error(y_test, preds_recursive)
  
imports: import numpy
  import pandas
  import pytest
  from sklearn.base import BaseEstimator, RegressorMixin
  from sklearn.dummy import DummyRegressor
  from sklearn.linear_model import LinearRegression
  from sklearn.pipeline import make_pipeline
  from sktime.datasets import load_airline
  from sktime.forecasting.base import ForecastingHorizon
  from sktime.forecasting.compose import DirectTabularRegressionForecaster, DirectTimeSeriesRegressionForecaster, DirRecTabularRegressionForecaster, DirRecTimeSeriesRegressionForecaster, MultioutputTabularRegressionForecaster, MultioutputTimeSeriesRegressionForecaster, RecursiveTabularRegressionForecaster, RecursiveTimeSeriesRegressionForecaster, make_reduction
  from sktime.forecasting.compose._reduce import _sliding_window_transform
  from sktime.forecasting.tests._config import TEST_OOS_FHS, TEST_WINDOW_LENGTHS_INT
  from sktime.performance_metrics.forecasting import mean_absolute_percentage_error
  from sktime.regression.base import BaseRegressor
  from sktime.regression.interval_based import TimeSeriesForestRegressor
  from sktime.split import SlidingWindowSplitter, temporal_train_test_split
  from sktime.split.tests.test_split import _get_windows
  from sktime.transformations.panel.reduce import Tabularizer
  from sktime.utils._testing.forecasting import make_forecasting_problem
  from sktime.utils.validation.forecasting import check_fh
label_desc: Use image node_id 15 for calling a global function with example usage: test_dirrec_against_recursive_accumulated_error() without return types