code: def test_results():
      endog = lake.copy()
      exog = np.c_[
          np.ones_like(endog), np.arange(1, len(endog) + 1) * 1.0
      ]
  
      # Test for results output
      p, res = gls(endog, exog, order=(1, 0, 0))
  
      assert_("params" in res)
      assert_("converged" in res)
      assert_("differences" in res)
      assert_("iterations" in res)
      assert_("arma_estimator" in res)
      assert_("arma_results" in res)
  
      assert_(res.converged)
      assert_(res.iterations > 0)
      assert_equal(res.arma_estimator, "innovations_mle")
      assert_equal(len(res.params), res.iterations + 1)
      assert_equal(len(res.differences), res.iterations + 1)
      assert_equal(len(res.arma_results), res.iterations + 1)
      assert_equal(res.params[-1], p)
  
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 5 for calling a global function with example usage: test_results() without return types