def test_AR_LD():
"""
Test the Levinson Durbin estimate of the AR coefficients against the
expercted PSD
"""
arsig, _, _ = utils.ar_generator(N=512)
avg_pwr = (arsig * arsig.conjugate()).real.mean()
order = 8
ak, sigma_v = tsa.AR_est_LD(arsig, order)
w, psd = tsa.AR_psd(ak, sigma_v)
# the psd is a one-sided power spectral density, which has been
# multiplied by 2 to preserve the property that
# 1/2pi int_{-pi}^{pi} Sxx(w) dw = Rxx(0)
# evaluate this integral numerically from 0 to pi
dw = np.pi / len(psd)
avg_pwr_est = np.trapz(psd, dx=dw) / (2 * np.pi)
npt.assert_almost_equal(avg_pwr, avg_pwr_est, decimal=0)
# Test for providing the autocovariance as an input:
ak, sigma_v = tsa.AR_est_LD(arsig, order, utils.autocov(arsig))
w, psd = tsa.AR_psd(ak, sigma_v)
avg_pwr_est = np.trapz(psd, dx=dw) / (2 * np.pi)
npt.assert_almost_equal(avg_pwr, avg_pwr_est, decimal=0)
def test_AR_est_consistency():
order = 10 # some even number
ak = _random_poles(order // 2)
x, v, _ = utils.ar_generator(N=512, coefs=-ak[1:], drop_transients=100)
ak_yw, ssq_yw = tsa.AR_est_YW(x, order)
ak_ld, ssq_ld = tsa.AR_est_LD(x, order)
npt.assert_almost_equal(ak_yw, ak_ld)
npt.assert_almost_equal(ssq_yw, ssq_ld)