code: def test_integrated():
      # Get the lake data
      endog1 = lake.copy()
      exog1 = np.c_[
          np.ones_like(endog1), np.arange(1, len(endog1) + 1) * 1.0
      ]
  
      endog2 = np.r_[0, np.cumsum(endog1)]
      exog2 = np.c_[[0, 0], np.cumsum(exog1, axis=0).T].T
  
      # Estimate without integration
      p1, _ = gls(endog1, exog1, order=(1, 0, 0))
  
      # Estimate with integration
      with assert_warns(UserWarning):
          p2, _ = gls(endog2, exog2, order=(1, 1, 0))
  
      assert_allclose(p1.params, p2.params)
  
file_path: statsmodels/statsmodels/tsa/arima/estimators/tests/test_gls.py
imports: import numpy
  import pytest
  from numpy.testing import assert_, assert_allclose, assert_equal, assert_warns, assert_raises
  from statsmodels.tsa.arima.datasets.brockwell_davis_2002 import lake, oshorts
  from statsmodels.tsa.arima.estimators.gls import gls
label_desc: Use image node_id 3 for calling a global function with example usage: test_integrated() without return types