code: def test_innovations():
      # Test for basic use of Yule-Walker estimation
      endog = dta["infl"].iloc[:50]
  
      # MA(2), no trend (since trend would imply GLS estimation)
      desired_p, _ = innovations(endog, ma_order=2, demean=False)
      mod = ARIMA(endog, order=(0, 0, 2), trend="n")
      res = mod.fit(method="innovations")
      assert_allclose(res.params, desired_p[-1].params)
  
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 6 for calling a global function with example usage: test_innovations() without return types