def obj(params):
p.params = spec.constrain_params(params)
return -arma_innovations.arma_loglike(
endog,
ar_params=-p.reduced_ar_poly.coef[1:],
ma_params=p.reduced_ma_poly.coef[1:],
sigma2=p.sigma2)
def test_innovations_algo_filter_kalman_filter(ar_params, ma_params, sigma2):
# Test the innovations algorithm and filter against the Kalman filter
# for exact likelihood evaluation of an ARMA process
endog = np.random.normal(size=100)
# Innovations algorithm approach
llf = arma_innovations.arma_loglike(endog, ar_params, ma_params, sigma2)
llf_obs = arma_innovations.arma_loglikeobs(endog, ar_params, ma_params,
sigma2)
score = arma_innovations.arma_score(endog, ar_params, ma_params, sigma2)
score_obs = arma_innovations.arma_scoreobs(endog, ar_params, ma_params,
sigma2)
# Kalman filter apparoach
mod = SARIMAX(endog, order=(len(ar_params), 0, len(ma_params)))
params = np.r_[ar_params, ma_params, sigma2]
# Test that the two approaches are the same
assert_allclose(llf, mod.loglike(params))
assert_allclose(llf_obs, mod.loglikeobs(params))
# Note: the tolerance on the two gets worse as more nobs are added
assert_allclose(score, mod.score(params), atol=1e-5)
assert_allclose(score_obs, mod.score_obs(params), atol=1e-5)