code: def test_bartlett_auto(data: ArrayLike):
      nw = Bartlett(data, force_int=True)
      if data.ndim == 1:
          expected_bw = 11
      else:
          expected_bw = 12
      assert int(nw.bandwidth) == expected_bw
      expected = 1.0 - np.arange(nw.bandwidth + 1) / (nw.bandwidth + 1)
      assert_allclose(nw.kernel_weights, expected)
      resid = data - np.asarray(data.mean(0))
      resid = np.asarray(resid)
      nobs = resid.shape[0]
      expected_cov = resid.T @ resid / nobs
      assert_allclose(expected_cov, np.squeeze(nw.cov.short_run))
      expected_oss = np.zeros_like(expected_cov)
      for i in range(1, int(nw.bandwidth) + 1):
          gamma = (resid[i:].T @ resid[:-i]) / nobs
          expected_oss += expected[i] * gamma
          expected_cov += expected[i] * (gamma + gamma.T)
      assert_allclose(expected_oss, np.squeeze(nw.cov.one_sided_strict))
      assert_allclose(expected_cov, np.squeeze(nw.cov.long_run))
      ce = CovarianceEstimate(
          short_run=np.asarray(nw.cov.short_run),
          one_sided_strict=np.asarray(nw.cov.one_sided_strict),
          long_run=np.asarray(nw.cov.long_run),
          one_sided=np.asarray(nw.cov.one_sided),
      )
      assert_allclose(ce.short_run, nw.cov.short_run)
      assert_allclose(ce.one_sided_strict, nw.cov.one_sided_strict)
      assert_allclose(ce.long_run, nw.cov.long_run)
      assert_allclose(ce.one_sided, nw.cov.one_sided)
  
file_path: arch/arch/tests/covariance/test_covariance.py
imports: from itertools import product
  import numpy
  from numpy.testing import assert_allclose
  import pandas
  import pytest
  from arch.covariance.kernel import Andrews, Bartlett, CovarianceEstimate, CovarianceEstimator, Gallant, NeweyWest, Parzen, ParzenCauchy, ParzenGeometric, ParzenRiesz, QuadraticSpectral, TukeyHamming, TukeyHanning, TukeyParzen
  from arch.typing import ArrayLike
label_desc: Use image node_id 5 for calling a global function with example usage: test_bartlett_auto(data) without return types