code: def check_itsmr(lake):
      # Test against R itsmr::yw; see results/results_yw_dl.R
      yw, _ = yule_walker(lake, 5)
  
      desired = [
          1.08213598501,
          -0.39658257147,
          0.11793957728,
          -0.03326633983,
          0.06209208707,
      ]
      assert_allclose(yw.ar_params, desired)
  
      # stats::ar.yw return the innovations algorithm estimate of the variance
      u, v = arma_innovations(
          np.array(lake) - np.mean(lake),
          ar_params=yw.ar_params,
          sigma2=1,
      )
      desired_sigma2 = 0.4716322564
      assert_allclose(np.sum(u**2 / v) / len(u), desired_sigma2)
  
file_path: statsmodels/statsmodels/tsa/arima/estimators/tests/test_yule_walker.py
imports: import numpy
  import pytest
  from numpy.testing import assert_allclose, assert_equal, assert_raises
  from statsmodels.tsa.stattools import acovf
  from statsmodels.tsa.innovations.arma_innovations import arma_innovations
  from statsmodels.tsa.arima.datasets.brockwell_davis_2002 import dowj, lake
  from statsmodels.tsa.arima.estimators.yule_walker import yule_walker
label_desc: Use image node_id 3 for calling a global function with example usage: check_itsmr(lake) without return types