code: def test_period_detection(default_kwargs):
      class_kwargs, _, _ = _to_class_kwargs(default_kwargs)
      mod = STL(**class_kwargs)
      res = mod.fit()
  
      del class_kwargs["period"]
      endog = class_kwargs["endog"]
      index = pd.date_range("1-1-1959", periods=348, freq=MONTH_END)
      class_kwargs["endog"] = pd.Series(endog, index=index)
      mod = STL(**class_kwargs)
  
      res_implicit_period = mod.fit()
      assert_allclose(res.seasonal, res_implicit_period.seasonal)
  
imports: from statsmodels.compat.pandas import MONTH_END
  import os
  import pickle
  import numpy
  from numpy.testing import assert_allclose
  import pandas
  import pytest
  from statsmodels.datasets import co2
  from statsmodels.tsa.seasonal import STL, DecomposeResult
label_desc: Use image node_id 18 for calling a global function with example usage: test_period_detection(default_kwargs) without return types