def test_time_varying_model(reset_randomstate):
endog = np.array([[0.5, 1.2, -0.2, 0.3, -0.1, 0.4, 1.4, 0.9],
[-0.2, -0.3, -0.1, 0.1, 0.01, 0.05, -0.13, -0.2]]).T
# The basic model switches to the univariate method at observation 3,
# because the forecast error covariance matrix will have a singular
# component corresponding to the first endog variable
np.random.seed(1234)
mod_switch = TVSS(endog)
mod_switch['design', ..., 3] = 0
mod_switch['obs_cov', ..., 3] = 0
mod_switch['obs_cov', 1, 1, 3] = 1.
res_switch = mod_switch.ssm.smooth()
kfilter = mod_switch.ssm._kalman_filter
uf_switch = np.array(kfilter.univariate_filter, copy=True)
# Next, this model only uses the univariate method
np.random.seed(1234)
mod_uv = TVSS(endog)
mod_uv['design', ..., 3] = 0
mod_uv['obs_cov', ..., 3] = 0
mod_uv['obs_cov', 1, 1, 3] = 1.
mod_uv.ssm.filter_univariate = True
res_uv = mod_uv.ssm.smooth()
kfilter = mod_uv.ssm._kalman_filter
uf_uv = np.array(kfilter.univariate_filter, copy=True)
# Finally, this model uses the multivariate method and gets around the
# issue by setting the endog variable to NaN that would have contributed
# to the singular part of the forecast error covariance matrix
np.random.seed(1234)
endog_mv = endog.copy()
endog_mv[3, 0] = np.nan
mod_mv = TVSS(endog_mv)
mod_mv['design', ..., 3] = 0
mod_mv['obs_cov', ..., 3] = 0
mod_mv['obs_cov', 1, 1, 3] = 1.
res_mv = mod_mv.ssm.smooth()
kfilter = mod_mv.ssm._kalman_filter
uf_mv = np.array(kfilter.univariate_filter, copy=True)
# Make sure that switching happened in the switch model but not in the
# other two models
assert_allclose(uf_switch[:3], 0)
assert_allclose(uf_switch[3], 1)
assert_allclose(uf_switch[4:], 0)
assert_allclose(uf_uv, 1)
assert_allclose(uf_mv, 0)
# Check filter and smoother output
check_filter_output([res_mv, res_switch, res_uv], np.s_[3])
check_smoother_output([res_mv, res_switch, res_uv], np.s_[3])
def test_nondiagonal_obs_cov(reset_randomstate):
# All diffuse handling is done using the univariate filtering approach,
# even if the usual multivariate filtering method is being used for the
# other periods. This means that if the observation covariance matrix is
# not a diagonal matrix during the diffuse periods, we need to transform
# the observation equation as we would if we were using the univariate
# filter.
mod = TVSS(np.zeros((10, 2)))
res1 = mod.smooth([])
mod.ssm.filter_univariate = True
res2 = mod.smooth([])
atol = 0.002 if PLATFORM_WIN else 1e-5
rtol = 0.002 if PLATFORM_WIN else 1e-6
# Here we'll just test a few values
assert_allclose(res1.llf, res2.llf, rtol=rtol, atol=atol)
assert_allclose(res1.forecasts[0], res2.forecasts[0],
rtol=rtol, atol=atol)
assert_allclose(res1.filtered_state, res2.filtered_state,
rtol=rtol, atol=atol)
assert_allclose(res1.filtered_state_cov, res2.filtered_state_cov,
rtol=rtol, atol=atol)
assert_allclose(res1.smoothed_state, res2.smoothed_state,
rtol=rtol, atol=atol)
assert_allclose(res1.smoothed_state_cov, res2.smoothed_state_cov,
rtol=rtol, atol=atol)
def test_smoothed_state_obs_weights_univariate_singular(singular, periods,
reset_randomstate):
# Tests for the univariate case when the forecast error covariance matrix
# is singular (so the multivariate approach cannot be used, and the use of
# pinv in computing the weights becomes actually operative)
endog = np.zeros((10, 2))
endog[6, 0] = np.nan
endog[7, :] = np.nan
endog[8, 1] = np.nan
mod = TVSS(endog)
mod.ssm.initialize_known([1.2, 0.8], np.eye(2) * 0)
if singular == 'both':
mod['obs_cov', ..., :periods] = 0
else:
mod['obs_cov', 0, 1, :periods] = 0
mod['obs_cov', 1, 0, :periods] = 0
mod['obs_cov', singular, singular, :periods] = 0
mod['state_cov', :, :, :periods] = 0
mod.ssm.filter_univariate = True
res = mod.smooth([])
# Make sure we actually have singular covariance matrices in the periods
# specified
for i in range(periods):
eigvals = np.linalg.eigvalsh(res.forecasts_error_cov[..., i])
assert_equal(np.min(eigvals), 0)
# Compute the desiried weights
n = mod.nobs
m = mod.k_states
p = mod.k_endog
desired = np.zeros((n, n, m, p)) * np.nan
# Here we manually compute the weights by adjusting one observation at a
# time
for j in range(n):
for i in range(p):
if np.isnan(endog[j, i]):
desired[:, j, :, i] = np.nan
else:
y = endog.copy()
y[j, i] = 1.0
tmp_mod = mod.clone(y)
tmp_mod.ssm.initialize_known([1.2, 0.8], np.eye(2) * 0)
tmp_mod.ssm.filter_univariate = True
tmp_res = tmp_mod.smooth([])
desired[:, j, :, i] = (tmp_res.smoothed_state.T
- res.smoothed_state.T)
actual, _, _ = tools.compute_smoothed_state_weights(res)
assert_allclose(actual, desired, atol=1e-12)
def test_compute_t_compute_j(compute_j, compute_t, reset_randomstate):
# Tests for the collapsed case
endog = np.zeros((10, 6))
endog[2, :] = np.nan
endog[6, 0] = np.nan
endog[7, :] = np.nan
endog[8, 1] = np.nan
mod = TVSS(endog)
mod['obs_intercept'] = np.zeros((6, 1))
mod.ssm.initialize_known([1.2, 0.8], np.eye(2))
mod.ssm.filter_collapsed = True
res = mod.smooth([])
# Compute the desiried weights
n = mod.nobs
m = mod.k_states
p = mod.k_endog
desired = np.zeros((n, n, m, p)) * np.nan
# Here we manually compute the weights by adjusting one observation at a
# time
for j in range(n):
for i in range(p):
if np.isnan(endog[j, i]):
desired[:, j, :, i] = np.nan
else:
y = endog.copy()
y[j, i] = 1.0
tmp_mod = mod.clone(y)
tmp_mod['obs_intercept'] = np.zeros((6, 1))
tmp_mod.ssm.initialize_known([1.2, 0.8], np.eye(2))
mod.ssm.filter_collapsed = True
tmp_res = tmp_mod.smooth([])
desired[:, j, :, i] = (tmp_res.smoothed_state.T
- res.smoothed_state.T)
actual, _, _ = tools.compute_smoothed_state_weights(
res, compute_t=compute_t, compute_j=compute_j)
compute_t = np.atleast_1d(compute_t)
compute_j = np.atleast_1d(compute_j)
for t in np.arange(10):
if t not in compute_t:
desired[t, :] = np.nan
for j in np.arange(10):
if j not in compute_j:
desired[:, j] = np.nan
assert_allclose(actual, desired, atol=1e-12)
def test_predicted_filtered_smoothed_TVSS(reset_randomstate):
mod = TVSS(np.zeros((50, 2)))
mod.ssm.initialize_known([1.2, 0.8], np.eye(2))
res = mod.smooth([])
mod_oos = TVSS(np.zeros((11, 2)) * np.nan)
kwargs = {
key: mod_oos[key]
for key in [
'obs_intercept', 'design', 'obs_cov', 'transition', 'selection',
'state_cov'
]
}
p_pred = res.get_prediction(start=0,
end=60,
information_set='predicted',
**kwargs)
f_pred = res.get_prediction(start=0,
end=60,
information_set='filtered',
**kwargs)
s_pred = res.get_prediction(start=0,
end=60,
information_set='smoothed',
**kwargs)
p_signal = res.get_prediction(start=0,
end=60,
information_set='predicted',
signal_only=True,
**kwargs)
f_signal = res.get_prediction(start=0,
end=60,
information_set='filtered',
signal_only=True,
**kwargs)
s_signal = res.get_prediction(start=0,
end=60,
information_set='smoothed',
signal_only=True,
**kwargs)
# Test forecasts and signals
d = mod['obs_intercept'].transpose(1, 0)[:, :, None]
Z = mod['design'].transpose(2, 0, 1)
H = mod['obs_cov'].transpose(2, 0, 1)
fcast = res.get_forecast(11, **kwargs)
fcast_signal = fcast.predicted_mean - mod_oos['obs_intercept'].T
fcast_signal_cov = fcast.var_pred_mean - mod_oos['obs_cov'].T
desired_s_signal = Z @ res.smoothed_state.T[:, :, None]
desired_f_signal = Z @ res.filtered_state.T[:, :, None]
desired_p_signal = Z @ res.predicted_state.T[:-1, :, None]
assert_allclose(s_pred.predicted_mean[:50], (d + desired_s_signal)[..., 0])
assert_allclose(s_pred.predicted_mean[50:], fcast.predicted_mean)
assert_allclose(f_pred.predicted_mean[:50], (d + desired_f_signal)[..., 0])
assert_allclose(f_pred.predicted_mean[50:], fcast.predicted_mean)
assert_allclose(p_pred.predicted_mean[:50], (d + desired_p_signal)[..., 0])
assert_allclose(p_pred.predicted_mean[50:], fcast.predicted_mean)
assert_allclose(s_signal.predicted_mean[:50], desired_s_signal[..., 0])
assert_allclose(s_signal.predicted_mean[50:], fcast_signal)
assert_allclose(f_signal.predicted_mean[:50], desired_f_signal[..., 0])
assert_allclose(f_signal.predicted_mean[50:], fcast_signal)
assert_allclose(p_signal.predicted_mean[:50], desired_p_signal[..., 0])
assert_allclose(p_signal.predicted_mean[50:], fcast_signal)
for t in range(mod.nobs):
assert_allclose(s_pred.var_pred_mean[t],
Z[t] @ res.smoothed_state_cov[..., t] @ Z[t].T + H[t])
assert_allclose(f_pred.var_pred_mean[t],
Z[t] @ res.filtered_state_cov[..., t] @ Z[t].T + H[t])
assert_allclose(p_pred.var_pred_mean[t],
Z[t] @ res.predicted_state_cov[..., t] @ Z[t].T + H[t])
assert_allclose(s_signal.var_pred_mean[t],
Z[t] @ res.smoothed_state_cov[..., t] @ Z[t].T)
assert_allclose(f_signal.var_pred_mean[t],
Z[t] @ res.filtered_state_cov[..., t] @ Z[t].T)
assert_allclose(p_signal.var_pred_mean[t],
Z[t] @ res.predicted_state_cov[..., t] @ Z[t].T)
assert_allclose(s_pred.var_pred_mean[50:], fcast.var_pred_mean)
assert_allclose(f_pred.var_pred_mean[50:], fcast.var_pred_mean)
assert_allclose(p_pred.var_pred_mean[50:], fcast.var_pred_mean)
assert_allclose(s_signal.var_pred_mean[50:], fcast_signal_cov)
assert_allclose(f_signal.var_pred_mean[50:], fcast_signal_cov)
assert_allclose(p_signal.var_pred_mean[50:], fcast_signal_cov)
def test_predicted_filtered_smoothed_with_nans_TVSS(reset_randomstate):
mod = TVSS(np.zeros((50, 2)) * np.nan)
mod.ssm.initialize_known([1.2, 0.8], np.eye(2))
res = mod.smooth([])
mod_oos = TVSS(np.zeros((11, 2)) * np.nan)
kwargs = {
key: mod_oos[key]
for key in [
'obs_intercept', 'design', 'obs_cov', 'transition', 'selection',
'state_cov'
]
}
p_pred = res.get_prediction(start=0,
end=60,
information_set='predicted',
**kwargs)
f_pred = res.get_prediction(start=0,
end=60,
information_set='filtered',
**kwargs)
s_pred = res.get_prediction(start=0,
end=60,
information_set='smoothed',
**kwargs)
# Test forecasts
assert_allclose(s_pred.predicted_mean, p_pred.predicted_mean)
assert_allclose(s_pred.var_pred_mean, p_pred.var_pred_mean)
assert_allclose(f_pred.predicted_mean, p_pred.predicted_mean)
assert_allclose(f_pred.var_pred_mean, p_pred.var_pred_mean)
assert_allclose(p_pred.predicted_mean[:50], res.fittedvalues)
assert_allclose(p_pred.var_pred_mean[:50].T, res.forecasts_error_cov)
p_signal = res.get_prediction(start=0,
end=60,
information_set='predicted',
signal_only=True,
**kwargs)
f_signal = res.get_prediction(start=0,
end=60,
information_set='filtered',
signal_only=True,
**kwargs)
s_signal = res.get_prediction(start=0,
end=60,
information_set='smoothed',
signal_only=True,
**kwargs)
# Test signal predictions
assert_allclose(s_signal.predicted_mean, p_signal.predicted_mean)
assert_allclose(s_signal.var_pred_mean, p_signal.var_pred_mean)
assert_allclose(f_signal.predicted_mean, p_signal.predicted_mean)
assert_allclose(f_signal.var_pred_mean, p_signal.var_pred_mean)
assert_allclose(p_signal.predicted_mean[:50] + mod['obs_intercept'].T,
res.fittedvalues)
assert_allclose((p_signal.var_pred_mean[:50] + mod['obs_cov'].T).T,
res.forecasts_error_cov)
def test_smoothed_state_obs_weights_collapsed(reset_randomstate):
# Tests for the collapsed case
endog = np.zeros((20, 6))
endog[2, :] = np.nan
endog[6, 0] = np.nan
endog[7, :] = np.nan
endog[8, 1] = np.nan
mod = TVSS(endog)
mod['obs_intercept'] = np.zeros((6, 1))
mod.ssm.initialize_known([1.2, 0.8], np.eye(2))
mod.ssm.filter_collapsed = True
res = mod.smooth([])
# Compute the desiried weights
n = mod.nobs
m = mod.k_states
p = mod.k_endog
desired = np.zeros((n, n, m, p)) * np.nan
# Here we manually compute the weights by adjusting one observation at a
# time
for j in range(n):
for i in range(p):
if np.isnan(endog[j, i]):
desired[:, j, :, i] = np.nan
else:
y = endog.copy()
y[j, i] = 1.0
tmp_mod = mod.clone(y)
tmp_mod['obs_intercept'] = np.zeros((6, 1))
tmp_mod.ssm.initialize_known([1.2, 0.8], np.eye(2))
mod.ssm.filter_collapsed = True
tmp_res = tmp_mod.smooth([])
desired[:, j, :, i] = (tmp_res.smoothed_state.T
- res.smoothed_state.T)
desired_state_intercept_weights = np.zeros((n, n, m, m)) * np.nan
# Here we manually compute the weights by adjusting one state intercept
# at a time
for j in range(n):
for ell in range(m):
tmp_mod = mod.clone(endog)
tmp_mod['obs_intercept'] = np.zeros((6, 1))
tmp_mod.ssm.initialize_known([1.2, 0.8], np.eye(2))
mod.ssm.filter_collapsed = True
if tmp_mod['state_intercept'].ndim == 1:
si = tmp_mod['state_intercept']
tmp_mod['state_intercept'] = np.zeros((mod.k_states, mod.nobs))
tmp_mod['state_intercept', :, :] = si[:, None]
tmp_mod['state_intercept', ell, j] += 1.0
tmp_res = tmp_mod.ssm.smooth()
desired_state_intercept_weights[:, j, :, ell] = (
tmp_res.smoothed_state.T - res.smoothed_state.T)
actual, actual_state_intercept_weights, _ = (
tools.compute_smoothed_state_weights(res))
assert_allclose(actual, desired, atol=1e-12)
assert_allclose(actual_state_intercept_weights,
desired_state_intercept_weights, atol=1e-12)
def test_smoothed_state_obs_weights_TVSS(univariate, diffuse,
reset_randomstate):
endog = np.zeros((10, 3))
# One simple way to introduce more diffuse periods is to have fully missing
# observations at the beginning
if diffuse == 4:
endog[:3] = np.nan
endog[6, 0] = np.nan
endog[7, :] = np.nan
endog[8, 1] = np.nan
mod = TVSS(endog)
prior_mean = np.array([1.2, 0.8])
prior_cov = np.eye(2)
if not diffuse:
mod.ssm.initialize_known(prior_mean, prior_cov)
if univariate:
mod.ssm.filter_univariate = True
res = mod.smooth([])
# Compute the desiried weights
n = mod.nobs
m = mod.k_states
p = mod.k_endog
desired = np.zeros((n, n, m, p)) * np.nan
# Here we manually compute the weights by adjusting one observation at a
# time
for j in range(n):
for i in range(p):
if np.isnan(endog[j, i]):
desired[:, j, :, i] = np.nan
else:
y = endog.copy()
y[j, i] = 1.0
tmp_mod = mod.clone(y)
if not diffuse:
tmp_mod.ssm.initialize_known(prior_mean, prior_cov)
if univariate:
tmp_mod.ssm.filter_univariate = True
tmp_res = tmp_mod.smooth([])
desired[:, j, :, i] = (tmp_res.smoothed_state.T
- res.smoothed_state.T)
desired_state_intercept_weights = np.zeros((n, n, m, m)) * np.nan
# Here we manually compute the weights by adjusting one state intercept
# at a time
for j in range(n):
for ell in range(m):
tmp_mod = mod.clone(endog)
if not diffuse:
tmp_mod.ssm.initialize_known(prior_mean, prior_cov)
if univariate:
tmp_mod.ssm.filter_univariate = True
if tmp_mod['state_intercept'].ndim == 1:
si = tmp_mod['state_intercept']
tmp_mod['state_intercept'] = np.zeros((mod.k_states, mod.nobs))
tmp_mod['state_intercept', :, :] = si[:, None]
tmp_mod['state_intercept', ell, j] += 1.0
tmp_res = tmp_mod.ssm.smooth()
desired_state_intercept_weights[:, j, :, ell] = (
tmp_res.smoothed_state.T - res.smoothed_state.T)
desired_prior_weights = np.zeros((n, m, m)) * np.nan
if not diffuse:
for i in range(m):
a = prior_mean.copy()
a[i] += 1
tmp_mod = mod.clone(endog)
tmp_mod.ssm.initialize_known(a, prior_cov)
tmp_res = tmp_mod.smooth([])
desired_prior_weights[:, :, i] = (tmp_res.smoothed_state.T
- res.smoothed_state.T)
if not diffuse:
mod.ssm.initialize_known(prior_mean, prior_cov)
actual, actual_state_intercept_weights, actual_prior_weights = (
tools.compute_smoothed_state_weights(res))
d = res.nobs_diffuse
assert_equal(d, diffuse)
if diffuse:
assert_allclose(actual[:d], np.nan, atol=1e-12)
assert_allclose(actual[:, :d], np.nan, atol=1e-12)
assert_allclose(actual_state_intercept_weights[:d], np.nan)
assert_allclose(actual_state_intercept_weights[:, :d], np.nan)
assert_allclose(actual_prior_weights, np.nan)
else:
# Test that the weights are the same
assert_allclose(actual_prior_weights, desired_prior_weights,
atol=1e-12)
# In the non-diffuse case, we can actually use the weights along with
# the prior and observations to compute the smoothed state directly,
# and then compare that to what was returned by the usual Kalman
# smoothing routines
# Note that TVSS sets the state intercept to zeros, so this does not
# test that, although those weights are tested separately, see above
# and below.
contribution_prior = np.nansum(
actual_prior_weights * prior_mean[None, None, :], axis=2)
contribution_endog = np.nansum(
actual * (endog - mod['obs_intercept'].T)[None, :, None, :],
axis=(1, 3))
computed_smoothed_state = contribution_prior + contribution_endog
assert_allclose(computed_smoothed_state, res.smoothed_state.T)
assert_allclose(actual[d:, d:], desired[d:, d:], atol=1e-12)
assert_allclose(actual_state_intercept_weights[d:, d:],
desired_state_intercept_weights[d:, d:], atol=1e-12)
def test_smoothed_decomposition_TVSS(univariate, reset_randomstate):
endog = np.zeros((10, 3))
endog[6, 0] = np.nan
endog[7, :] = np.nan
endog[8, 1] = np.nan
mod = TVSS(endog)
mod['state_intercept'] = np.random.normal(size=(mod.k_states, mod.nobs))
prior_mean = np.array([1.2, 0.8])
prior_cov = np.eye(2)
mod.ssm.initialize_known(prior_mean, prior_cov)
if univariate:
mod.ssm.filter_univariate = True
res = mod.smooth([])
# Check smoothed state
# Get the decomposition of the smoothed state
cd, coi, csi, cp = res.get_smoothed_decomposition(
decomposition_of='smoothed_state')
# Sum across contributions (i.e. from observations at each time period and
# from the initial state)
css = ((cd + coi).sum(axis=1) + csi.sum(axis=1) + cp.sum(axis=1))
css = css.unstack(level='state_to')[mod.state_names].values
# Summing up all contributions should yield the actual smoothed state,
# so the smoothed state vector is the desired result of this test
ss = np.array(res.states.smoothed)
assert_allclose(css, ss, atol=1e-12)
# Check smoothed signal
# Use the summed state contributions and multiply by the design matrix
# to get the smoothed signal
cs_sig = (css.T * mod['design']).sum(axis=1).T
# Add in the observation intercept to get the smoothed forecast
csf = cs_sig + mod['obs_intercept'].T
# Summing up all contributions should yield the smoothed prediction of
# the observed variables
s_sig = res.predict(information_set='smoothed', signal_only=True)
sf = res.predict(information_set='smoothed', signal_only=False)
assert_allclose(cs_sig, s_sig, atol=1e-12)
assert_allclose(csf, sf, atol=1e-12)
# Now check the smoothed signal against the sum computed from the
# decomposed smoothed signal
cd, coi, csi, cp = res.get_smoothed_decomposition(
decomposition_of='smoothed_signal')
# Sum across contributions (i.e. from observations and intercepts at each
# time period and from the initial state) to get the smoothed signal
cs_sig = ((cd + coi).sum(axis=1) + csi.sum(axis=1) + cp.sum(axis=1))
cs_sig = cs_sig.unstack(level='variable_to')[mod.endog_names].values
assert_allclose(cs_sig, s_sig, atol=1e-12)
# Add in the observation intercept to get the smoothed forecast
csf = cs_sig + mod['obs_intercept'].T
assert_allclose(csf, sf)