code: def test_predict_interval_output_ForecasterSarimax_pmdarima_ARIMA(
      alpha, interval
  ):
      """
      Test predict_interval output of ForecasterSarimax using ARIMA from pmdarima.
      """
      forecaster = ForecasterSarimax(
          regressor=ARIMA(
              maxiter=1000,
              trend=None,
              method="nm",
              #    ftol      = 1e-19,
              order=(1, 1, 1),
          )
      )
      forecaster.fit(y=y)
      predictions = forecaster.predict_interval(
          steps=5, alpha=alpha, interval=interval
      )
      expected = pd.DataFrame(
          data=np.array(
              [
                  [0.66306615, 0.44125671, 0.88487559],
                  [0.69348775, 0.43388917, 0.95308633],
                  [0.71345977, 0.4407784, 0.98614114],
                  [0.72726861, 0.4495056, 1.00503162],
                  [0.7374424, 0.45753824, 1.01734656],
              ]
          ),
          columns=["pred", "lower_bound", "upper_bound"],
          index=pd.RangeIndex(start=50, stop=55, step=1),
      )
  
      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 5 for calling a global function with example usage: test_predict_interval_output_ForecasterSarimax_pmdarima_ARIMA(alpha, interval) without return types