def test_multivariate_acovf():
_acovf = tools._compute_multivariate_acovf_from_coefficients
# Test for a VAR(1) process. From Lutkepohl (2007), pages 27-28.
# See (2.1.14) for Phi_1, (2.1.33) for Sigma_u, and (2.1.34) for Gamma_0
Sigma_u = np.array([[2.25, 0, 0],
[0, 1.0, 0.5],
[0, 0.5, 0.74]])
Phi_1 = np.array([[0.5, 0, 0],
[0.1, 0.1, 0.3],
[0, 0.2, 0.3]])
Gamma_0 = np.array([[3.0, 0.161, 0.019],
[0.161, 1.172, 0.674],
[0.019, 0.674, 0.954]])
assert_allclose(_acovf([Phi_1], Sigma_u)[0], Gamma_0, atol=1e-3)
# Test for a VAR(2) process. From Lutkepohl (2007), pages 28-29
# See (2.1.40) for Phi_1, Phi_2, (2.1.14) for Sigma_u, and (2.1.42) for
# Gamma_0, Gamma_1
Sigma_u = np.diag([0.09, 0.04])
Phi_1 = np.array([[0.5, 0.1],
[0.4, 0.5]])
Phi_2 = np.array([[0, 0],
[0.25, 0]])
Gamma_0 = np.array([[0.131, 0.066],
[0.066, 0.181]])
Gamma_1 = np.array([[0.072, 0.051],
[0.104, 0.143]])
Gamma_2 = np.array([[0.046, 0.040],
[0.113, 0.108]])
Gamma_3 = np.array([[0.035, 0.031],
[0.093, 0.083]])
assert_allclose(
_acovf([Phi_1, Phi_2], Sigma_u, maxlag=0),
[Gamma_0], atol=1e-3)
assert_allclose(
_acovf([Phi_1, Phi_2], Sigma_u, maxlag=1),
[Gamma_0, Gamma_1], atol=1e-3)
assert_allclose(
_acovf([Phi_1, Phi_2], Sigma_u),
[Gamma_0, Gamma_1], atol=1e-3)
assert_allclose(
_acovf([Phi_1, Phi_2], Sigma_u, maxlag=2),
[Gamma_0, Gamma_1, Gamma_2], atol=1e-3)
assert_allclose(
_acovf([Phi_1, Phi_2], Sigma_u, maxlag=3),
[Gamma_0, Gamma_1, Gamma_2, Gamma_3], atol=1e-3)
# Test sample acovf in the univariate case against sm.tsa.acovf
x = np.arange(20)*1.0
assert_allclose(
np.squeeze(tools._compute_multivariate_sample_acovf(x, maxlag=4)),
acovf(x)[:5])
def test_multivariate_acovf():
_acovf = tools._compute_multivariate_acovf_from_coefficients
# Test for a VAR(1) process. From Lutkepohl (2007), pages 27-28.
# See (2.1.14) for Phi_1, (2.1.33) for Sigma_u, and (2.1.34) for Gamma_0
Sigma_u = np.array([[2.25, 0, 0],
[0, 1.0, 0.5],
[0, 0.5, 0.74]])
Phi_1 = np.array([[0.5, 0, 0],
[0.1, 0.1, 0.3],
[0, 0.2, 0.3]])
Gamma_0 = np.array([[3.0, 0.161, 0.019],
[0.161, 1.172, 0.674],
[0.019, 0.674, 0.954]])
assert_allclose(_acovf([Phi_1], Sigma_u)[0], Gamma_0, atol=1e-3)
# Test for a VAR(2) process. From Lutkepohl (2007), pages 28-29
# See (2.1.40) for Phi_1, Phi_2, (2.1.14) for Sigma_u, and (2.1.42) for
# Gamma_0, Gamma_1
Sigma_u = np.diag([0.09, 0.04])
Phi_1 = np.array([[0.5, 0.1],
[0.4, 0.5]])
Phi_2 = np.array([[0, 0],
[0.25, 0]])
Gamma_0 = np.array([[0.131, 0.066],
[0.066, 0.181]])
Gamma_1 = np.array([[0.072, 0.051],
[0.104, 0.143]])
Gamma_2 = np.array([[0.046, 0.040],
[0.113, 0.108]])
Gamma_3 = np.array([[0.035, 0.031],
[0.093, 0.083]])
assert_allclose(
_acovf([Phi_1, Phi_2], Sigma_u, maxlag=0),
[Gamma_0], atol=1e-3)
assert_allclose(
_acovf([Phi_1, Phi_2], Sigma_u, maxlag=1),
[Gamma_0, Gamma_1], atol=1e-3)
assert_allclose(
_acovf([Phi_1, Phi_2], Sigma_u),
[Gamma_0, Gamma_1], atol=1e-3)
assert_allclose(
_acovf([Phi_1, Phi_2], Sigma_u, maxlag=2),
[Gamma_0, Gamma_1, Gamma_2], atol=1e-3)
assert_allclose(
_acovf([Phi_1, Phi_2], Sigma_u, maxlag=3),
[Gamma_0, Gamma_1, Gamma_2, Gamma_3], atol=1e-3)
# Test sample acovf in the univariate case against sm.tsa.acovf
x = np.arange(20)*1.0
assert_allclose(
np.squeeze(tools._compute_multivariate_sample_acovf(x, maxlag=4)),
acovf(x)[:5])