code: def test_append_with_exog():
      # Numpy
      endog = dta["infl"].iloc[:100].values
      exog = np.arange(len(endog))
      mod = ARIMA(endog[:50], exog=exog[:50], trend="c")
      res = mod.fit()
      res_e = res.append(endog[50:], exog=exog[50:])
      mod2 = ARIMA(endog, exog=exog, trend="c")
      res2 = mod2.filter(res_e.params)
  
      assert_allclose(res2.llf, res_e.llf)
  
imports: from statsmodels.compat.platform import PLATFORM_WIN32
  import io
  import numpy
  import pandas
  import pytest
  from numpy.testing import assert_equal, assert_allclose, assert_raises, assert_
  from statsmodels.datasets import macrodata
  from statsmodels.tsa.arima.model import ARIMA
  from statsmodels.tsa.arima.estimators.yule_walker import yule_walker
  from statsmodels.tsa.arima.estimators.burg import burg
  from statsmodels.tsa.arima.estimators.hannan_rissanen import hannan_rissanen
  from statsmodels.tsa.arima.estimators.innovations import innovations, innovations_mle
  from statsmodels.tsa.arima.estimators.statespace import statespace
label_desc: Use image node_id 16 for calling a global function with example usage: test_append_with_exog() without return types