code: def test_auto_bandwidth(trivariate_data):
      y, x = trivariate_data
      res = phillips_ouliaris(y, x)
      assert isinstance(res.summary(), Summary)
      assert int(res.bandwidth) != res.bandwidth
      res = phillips_ouliaris(y, x, force_int=True)
      assert int(res.bandwidth) == res.bandwidth
  
file_path: arch/arch/tests/unitroot/test_phillips_ouliaris.py
imports: import numpy
  from numpy.testing import assert_allclose
  import pytest
  from statsmodels.iolib.summary import Summary
  from arch.typing import Float64Array, UnitRootTrend
  from arch.unitroot._phillips_ouliaris import CriticalValueWarning, phillips_ouliaris_cv, phillips_ouliaris_pval
  from arch.unitroot.cointegration import phillips_ouliaris
  from arch.utility.timeseries import add_trend
label_desc: Use image node_id 10 for calling a global function with example usage: test_auto_bandwidth(trivariate_data) without return types