code: def test_Sarimax_fit_with_numpy():
      """
      Test Sarimax fit with numpy `y` and `exog`.
      """
  
      sarimax = Sarimax(order=(1, 1, 1))
  
      assert sarimax.output_type is None
      assert sarimax.sarimax_res is None
      assert sarimax.fitted == False
      assert sarimax.training_index is None
  
      sarimax.fit(y=y_numpy, exog=exog_numpy)
  
      assert sarimax.output_type == "numpy"
      assert isinstance(sarimax.sarimax_res, SARIMAXResultsWrapper)
      assert sarimax.fitted == True
      assert sarimax.training_index == None
  
imports: import re
  import pytest
  import numpy
  import pandas
  from sklearn.exceptions import NotFittedError
  from skforecast.Sarimax import Sarimax
  from statsmodels.tsa.statespace.sarimax import SARIMAX
  from statsmodels.tsa.statespace.sarimax import SARIMAXResults
  from statsmodels.tsa.statespace.sarimax import SARIMAXResultsWrapper
  from .fixtures_Sarimax import y
  from .fixtures_Sarimax import y_lw
  from .fixtures_Sarimax import exog
  from .fixtures_Sarimax import exog_lw
  from .fixtures_Sarimax import exog_predict
  from .fixtures_Sarimax import exog_lw_predict
  from .fixtures_Sarimax import y_datetime
  from .fixtures_Sarimax import exog_datetime
  from .fixtures_Sarimax import exog_predict_datetime
label_desc: Use image node_id 8 for calling a global function with example usage: test_Sarimax_fit_with_numpy() without return types