code: def test_convergence_simple():
      # issue 6883
      gen = np.random.RandomState(0)
      e = gen.standard_normal(12000)
      y = e.copy()
      for i in range(1, e.shape[0]):
          y[i] = y[i - 1] - 0.2 * e[i - 1] + e[i]
      y = y[200:]
      mod = holtwinters.ExponentialSmoothing(
          y, initialization_method="estimated"
      )
      res = mod.fit()
      ets_res = ETSModel(y).fit()
  
      # the smoothing level should be very similar, the initial state might be
      # different as it doesn't influence the final result too much
      assert_allclose(
          res.params["smoothing_level"],
          ets_res.smoothing_level,
          rtol=1e-4,
          atol=1e-4,
      )
  
      # the first few values are influenced by differences in initial state, so
      # we don't test them here
      assert_allclose(
          res.fittedvalues[10:],
          ets_res.fittedvalues[10:],
          rtol=1e-4,
          atol=1e-4,
      )
  
imports: from statsmodels.compat.pandas import QUARTER_END
  from statsmodels.compat.platform import PLATFORM_LINUX32, PLATFORM_WIN
  from itertools import product
  import json
  import pathlib
  import numpy
  from numpy.testing import assert_allclose, assert_almost_equal
  import pandas
  import pytest
  import scipy.stats
  from statsmodels.tsa.exponential_smoothing.ets import ETSModel
  import statsmodels.tsa.holtwinters
  import statsmodels.tsa.statespace.exponential_smoothing
label_desc: Use image node_id 38 for calling a global function with example usage: test_convergence_simple() without return types