code: def test_innovations_mle_misc():
      endog = np.arange(20) ** 2 * 1.0
  
      # Check that when Hannan-Rissanen estimates non-stationary starting
      # parameters, innovations_mle sets it to zero
      hr, _ = hannan_rissanen(endog, ar_order=1, demean=False)
      assert_(hr.ar_params[0] > 1)
      _, res = innovations_mle(endog, order=(1, 0, 0))
      assert_allclose(res.start_params[0], 0)
  
      # Check that when Hannan-Rissanen estimates non-invertible starting
      # parameters, innovations_mle sets it to zero
      hr, _ = hannan_rissanen(endog, ma_order=1, demean=False)
      assert_(hr.ma_params[0] > 1)
      _, res = innovations_mle(endog, order=(0, 0, 1))
      assert_allclose(res.start_params[0], 0)
  
imports: import numpy
  import pytest
  from numpy.testing import assert_, assert_allclose, assert_warns, assert_raises
  from statsmodels.tsa.innovations.arma_innovations import arma_innovations
  from statsmodels.tsa.statespace import sarimax
  from statsmodels.tsa.arima.datasets.brockwell_davis_2002 import dowj, lake, oshorts
  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
label_desc: Use image node_id 13 for calling a global function with example usage: test_innovations_mle_misc() without return types