code: def test_create_train_X_y_output_when_y_and_exog_no_pandas_index():
      """
      Test the output of create_train_X_y when y and exog have no pandas index
      that doesn't start at 0.
      """
      y = pd.Series(np.arange(10), index=np.arange(6, 16), dtype=float)
      exog = pd.Series(
          np.arange(100, 110),
          index=np.arange(6, 16),
          name="exog",
          dtype=float,
      )
  
      forecaster = ForecasterAutoregDirect(
          LinearRegression(), lags=3, steps=1
      )
      results = forecaster.create_train_X_y(y=y, exog=exog)
  
      expected = (
          pd.DataFrame(
              data=np.array(
                  [
                      [2.0, 1.0, 0.0, 103.0],
                      [3.0, 2.0, 1.0, 104.0],
                      [4.0, 3.0, 2.0, 105.0],
                      [5.0, 4.0, 3.0, 106.0],
                      [6.0, 5.0, 4.0, 107.0],
                      [7.0, 6.0, 5.0, 108.0],
                      [8.0, 7.0, 6.0, 109.0],
                  ],
                  dtype=float,
              ),
              index=pd.RangeIndex(start=3, stop=10, step=1),
              columns=["lag_1", "lag_2", "lag_3", "exog_step_1"],
          ),
          {
              1: pd.Series(
                  data=np.array(
                      [3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0], dtype=float
                  ),
                  index=pd.RangeIndex(start=3, stop=10, step=1),
                  name="y_step_1",
              )
          },
      )
  
      pd.testing.assert_frame_equal(results[0], expected[0])
      assert isinstance(results[1], dict)
      assert all(isinstance(x, pd.Series) for x in results[1].values())
      assert results[1].keys() == expected[1].keys()
      for key in expected[1]:
          pd.testing.assert_series_equal(
              results[1][key], expected[1][key]
          )
  
imports: import re
  import pytest
  import numpy
  import pandas
  from skforecast.ForecasterAutoregDirect import ForecasterAutoregDirect
  from skforecast.exceptions import MissingValuesExogWarning
  from sklearn.linear_model import LinearRegression
  from sklearn.compose import ColumnTransformer
  from sklearn.preprocessing import StandardScaler
  from sklearn.preprocessing import OneHotEncoder
label_desc: Use image node_id 8 for calling a global function with example usage: test_create_train_X_y_output_when_y_and_exog_no_pandas_index() without return types