code: def test_predict_interval_output_ForecasterSarimax_with_last_window(
      alpha, interval
  ):
      """
      Test predict_interval output of ForecasterSarimax with `last_window`.
      """
      forecaster = ForecasterSarimax(
          regressor=Sarimax(
              maxiter=1000, method="cg", disp=False, order=(3, 2, 0)
          )
      )
      forecaster.fit(y=y_datetime)
      predictions = forecaster.predict_interval(
          steps=5,
          alpha=alpha,
          interval=interval,
          last_window=y_lw_datetime,
      )
  
      expected = pd.DataFrame(
          data=np.array(
              [
                  [0.91877817, 0.62343187, 1.21412446],
                  [0.98433512, 0.49607518, 1.47259506],
                  [1.06945921, 0.40495001, 1.73396842],
                  [1.15605055, 0.27574629, 2.03635481],
                  [1.22975713, 0.08768469, 2.37182957],
              ]
          ),
          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 12 for calling a global function with example usage: test_predict_interval_output_ForecasterSarimax_with_last_window(alpha, interval) without return types