code: def test_multivariate_pacf():
      # Test sample acovf in the univariate case against sm.tsa.acovf
      np.random.seed(1234)
      x = np.arange(10000)
      y = np.random.normal(size=10000)
      # Note: could make this test more precise with higher nobs, but no need to
      assert_allclose(
          tools._compute_multivariate_sample_pacf(
              np.c_[x, y], maxlag=1
          )[0],
          np.diag([1, 0]),
          atol=1e-2,
      )
  
imports: import pytest
  import numpy
  from numpy.testing import assert_allclose, assert_equal, assert_array_less, assert_array_equal, assert_almost_equal
  import pandas
  from scipy.linalg import solve_discrete_lyapunov
  from statsmodels.tsa.statespace import tools
  from statsmodels.tsa.stattools import acovf
label_desc: Use image node_id 2 for calling a global function with example usage: test_multivariate_pacf() without return types