def test_innovations_filter_pandas(reset_randomstate):
ma = np.array([-0.9, 0.5])
acovf = np.array([1 + (ma**2).sum(), ma[0] + ma[1] * ma[0], ma[1]])
theta, _ = innovations_algo(acovf, nobs=10)
endog = np.random.randn(10)
endog_pd = pd.Series(endog, index=pd.date_range('2000-01-01', periods=10))
resid = innovations_filter(endog, theta)
resid_pd = innovations_filter(endog_pd, theta)
assert_allclose(resid, resid_pd.values)
assert_index_equal(endog_pd.index, resid_pd.index)
def test_innovations_filter_pandas(reset_randomstate):
ma = np.array([-0.9, 0.5])
acovf = np.array([1 + (ma ** 2).sum(), ma[0] + ma[1] * ma[0], ma[1]])
theta, _ = innovations_algo(acovf, nobs=10)
endog = np.random.randn(10)
endog_pd = pd.Series(endog,
index=pd.date_range('2000-01-01', periods=10))
resid = innovations_filter(endog, theta)
resid_pd = innovations_filter(endog_pd, theta)
assert_allclose(resid, resid_pd.values)
assert_index_equal(endog_pd.index, resid_pd.index)
def test_innovations_algo_filter_kalman_filter(reset_randomstate):
# Test the innovations algorithm and filter against the Kalman filter
# for exact likelihood evaluation of an ARMA process
ar_params = np.array([0.5])
ma_params = np.array([0.2])
# TODO could generalize to sigma2 != 1, if desired, after #5324 is merged
# and there is a sigma2 argument to arma_acovf
# (but maybe this is not really necessary for the point of this test)
sigma2 = 1
endog = np.random.normal(size=10)
# Innovations algorithm approach
acovf = arma_acovf(np.r_[1, -ar_params], np.r_[1, ma_params],
nobs=len(endog))
theta, v = innovations_algo(acovf)
u = innovations_filter(endog, theta)
llf_obs = -0.5 * u ** 2 / (sigma2 * v) - 0.5 * np.log(2 * np.pi * v)
# Kalman filter apparoach
mod = SARIMAX(endog, order=(len(ar_params), 0, len(ma_params)))
res = mod.filter(np.r_[ar_params, ma_params, sigma2])
# Test that the two approaches are identical
atol = 1e-6 if PLATFORM_WIN else 0.0
assert_allclose(u, res.forecasts_error[0], rtol=1e-6, atol=atol)
assert_allclose(theta[1:, 0], res.filter_results.kalman_gain[0, 0, :-1],
atol=atol)
assert_allclose(llf_obs, res.llf_obs, atol=atol)
def test_innovations_algo_filter_kalman_filter(reset_randomstate):
# Test the innovations algorithm and filter against the Kalman filter
# for exact likelihood evaluation of an ARMA process
ar_params = np.array([0.5])
ma_params = np.array([0.2])
# TODO could generalize to sigma2 != 1, if desired, after #5324 is merged
# and there is a sigma2 argument to arma_acovf
# (but maybe this is not really necessary for the point of this test)
sigma2 = 1
endog = np.random.normal(size=10)
# Innovations algorithm approach
acovf = arma_acovf(np.r_[1, -ar_params], np.r_[1, ma_params],
nobs=len(endog))
theta, v = innovations_algo(acovf)
u = innovations_filter(endog, theta)
llf_obs = -0.5 * u**2 / (sigma2 * v) - 0.5 * np.log(2 * np.pi * v)
# Kalman filter apparoach
mod = SARIMAX(endog, order=(len(ar_params), 0, len(ma_params)))
res = mod.filter(np.r_[ar_params, ma_params, sigma2])
# Test that the two approaches are identical
atol = 1e-6 if PLATFORM_WIN else 0.0
assert_allclose(u, res.forecasts_error[0], atol=atol)
assert_allclose(theta[1:, 0], res.filter_results.kalman_gain[0, 0, :-1],
atol=atol)
assert_allclose(llf_obs, res.llf_obs, atol=atol)
def test_innovations_filter_brockwell_davis(reset_randomstate):
ma = -0.9
acovf = np.array([1 + ma ** 2, ma])
theta, _ = innovations_algo(acovf, nobs=4)
e = np.random.randn(5)
endog = e[1:] + ma * e[:-1]
resid = innovations_filter(endog, theta)
expected = [endog[0]]
for i in range(1, 4):
expected.append(endog[i] - theta[i, 0] * expected[-1])
expected = np.array(expected)
assert_allclose(resid, expected)
def test_innovations_filter_brockwell_davis(reset_randomstate):
ma = -0.9
acovf = np.array([1 + ma ** 2, ma])
theta, _ = innovations_algo(acovf, nobs=4)
e = np.random.randn(5)
endog = e[1:] + ma * e[:-1]
resid = innovations_filter(endog, theta)
expected = [endog[0]]
for i in range(1, 4):
expected.append(endog[i] - theta[i, 0] * expected[-1])
expected = np.array(expected)
assert_allclose(resid, expected)
def test_innovations_filter_errors():
ma = -0.9
acovf = np.array([1 + ma ** 2, ma])
theta, _ = innovations_algo(acovf, nobs=4)
with pytest.raises(ValueError):
innovations_filter(np.empty((2, 2)), theta)
with pytest.raises(ValueError):
innovations_filter(np.empty(4), theta[:-1])
with pytest.raises(ValueError):
innovations_filter(pd.DataFrame(np.empty((1, 4))), theta)
def test_innovations_filter_errors():
ma = -0.9
acovf = np.array([1 + ma ** 2, ma])
theta, _ = innovations_algo(acovf, nobs=4)
with pytest.raises(ValueError):
innovations_filter(np.empty((2, 2)), theta)
with pytest.raises(ValueError):
innovations_filter(np.empty(4), theta[:-1])
with pytest.raises(ValueError):
innovations_filter(pd.DataFrame(np.empty((1, 4))), theta)
