code: def test_predict_interval_output_ForecasterSarimax_with_last_window_and_exog_and_transformers(
      alpha, interval
  ):
      """
      Test predict_interval output of ForecasterSarimax with exogenous variables and `last_window`.
      """
      transformer_exog = ColumnTransformer(
          [
              ("scale", StandardScaler(), ["exog_1"]),
              ("onehot", OneHotEncoder(), ["exog_2"]),
          ],
          remainder="passthrough",
          verbose_feature_names_out=False,
      )
  
      forecaster = ForecasterSarimax(
          regressor=Sarimax(
              maxiter=1000, method="cg", disp=False, order=(1, 1, 1)
          ),
          transformer_y=StandardScaler(),
          transformer_exog=transformer_exog,
      )
      forecaster.fit(y=y_datetime, exog=df_exog_datetime)
      predictions = forecaster.predict_interval(
          steps=5,
          alpha=alpha,
          interval=interval,
          exog=df_exog_lw_predict_datetime,
          last_window=y_lw_datetime,
          last_window_exog=df_exog_lw_datetime,
      )
  
      expected = pd.DataFrame(
          data=np.array(
              [
                  [0.61139264, 0.35457567, 0.86820961],
                  [0.88228163, 0.57163268, 1.19293057],
                  [0.77749663, 0.42990006, 1.12509319],
                  [0.94985823, 0.58885008, 1.31086638],
                  [0.89218798, 0.5184476, 1.26592836],
              ]
          ),
          columns=["pred", "lower_bound", "upper_bound"],
          index=pd.date_range(start="2100", periods=5, freq="A"),
      )
  
      pd.testing.assert_frame_equal(predictions, expected, atol=0.0001)
  
imports: import re
  import pytest
  import numpy
  import pandas
  from sklearn.exceptions import NotFittedError
  from pmdarima.arima import ARIMA
  from skforecast.Sarimax import Sarimax
  from skforecast.ForecasterSarimax import ForecasterSarimax
  from skforecast.utils import expand_index
  from sklearn.compose import ColumnTransformer
  from sklearn.preprocessing import StandardScaler
  from sklearn.preprocessing import OneHotEncoder
  from .fixtures_ForecasterSarimax import y
  from .fixtures_ForecasterSarimax import y_lw
  from .fixtures_ForecasterSarimax import exog
  from .fixtures_ForecasterSarimax import exog_lw
  from .fixtures_ForecasterSarimax import exog_predict
  from .fixtures_ForecasterSarimax import exog_lw_predict
  from .fixtures_ForecasterSarimax import y_datetime
  from .fixtures_ForecasterSarimax import y_lw_datetime
  from .fixtures_ForecasterSarimax import exog_datetime
  from .fixtures_ForecasterSarimax import exog_lw_datetime
  from .fixtures_ForecasterSarimax import exog_predict_datetime
  from .fixtures_ForecasterSarimax import exog_lw_predict_datetime
  from .fixtures_ForecasterSarimax import df_exog
  from .fixtures_ForecasterSarimax import df_exog_lw
  from .fixtures_ForecasterSarimax import df_exog_predict
  from .fixtures_ForecasterSarimax import df_exog_lw_predict
  from .fixtures_ForecasterSarimax import df_exog_datetime
  from .fixtures_ForecasterSarimax import df_exog_lw_datetime
  from .fixtures_ForecasterSarimax import df_exog_predict_datetime
  from .fixtures_ForecasterSarimax import df_exog_lw_predict_datetime
label_desc: Use image node_id 14 for calling a global function with example usage: test_predict_interval_output_ForecasterSarimax_with_last_window_and_exog_and_transformers(alpha, interval) without return types