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"""
Tests for automatic switching of the filter method from multivariate to
univariate when the forecast error covariance matrix is singular.
Author: Chad Fulton
License: Simplified-BSD
References
----------
Kim, Chang-Jin, and Charles R. Nelson. 1999.
"State-Space Models with Regime Switching:
Classical and Gibbs-Sampling Approaches with Applications".
MIT Press Books. The MIT Press.
Hamilton, James D. 1994.
Time Series Analysis.
Princeton, N.J.: Princeton University Press.
"""
import numpy as np
import pytest
import sys
import platform
import re
i386_looser_tolerances=bool(re.match('i.?86|x86',platform.uname()[4])) and np.log2(sys.maxsize)<33
from statsmodels.tsa.statespace import (
mlemodel, sarimax, structural, varmax, dynamic_factor)
from statsmodels.tsa.statespace.tests.test_impulse_responses import TVSS
from numpy.testing import assert_allclose
def get_model(univariate, missing=None, init=None):
if univariate:
endog = np.array([0.5, 1.2, -0.2, 0.3, -0.1, 0.4, 1.4, 0.9])
if missing == 'init':
endog[0:2] = np.nan
elif missing == 'mixed':
endog[2:4] = np.nan
elif missing == 'all':
endog[:] = np.nan
mod = mlemodel.MLEModel(endog, k_states=1, k_posdef=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 0.5
mod['selection', 0, 0] = 1.
mod['state_cov', 0, 0] = 1.
mod['state_intercept', 0, 0] = 1.
else:
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
if missing == 'init':
endog[0:2, :] = np.nan
elif missing == 'mixed':
endog[2:4, 0] = np.nan
endog[3:6, 1] = np.nan
elif missing == 'all':
endog[:] = np.nan
mod = mlemodel.MLEModel(endog, k_states=3, k_posdef=2)
mod['obs_intercept'] = np.array([0.5, 0.2])
mod['design'] = np.array([[0.1, -0.1, 0],
[0.2, 0.3, 0]])
mod['obs_cov'] = np.array([[5, -0.2],
[-0.2, 3.]])
mod['transition', 0, 0] = 1
mod['transition', 1:, 1:] = np.array([[0.5, -0.1],
[1., 0.]])
mod['selection', :2, :2] = np.eye(2)
mod['state_cov'] = np.array([[1.2, 0.2],
[0.2, 2.5]])
mod['state_intercept', :2] = np.array([1., -1.])
if init == 'diffuse':
mod.ssm.initialize_diffuse()
elif init == 'approximate_diffuse':
mod.ssm.initialize_approximate_diffuse()
elif init == 'stationary':
mod.ssm.initialize_stationary()
return mod
def check_filter_output(mod, periods, atol=0):
if isinstance(mod, mlemodel.MLEModel):
# Multivariate filter
res_mv = mod.ssm.filter()
# Manually perform filtering with a switch
mod.ssm.filter()
kfilter = mod.ssm._kalman_filter
kfilter.seek(0, True)
kfilter.univariate_filter[periods] = 1
for _ in range(mod.nobs):
next(kfilter)
# Create the results object
res_switch = mod.ssm.results_class(mod.ssm)
res_switch.update_representation(mod.ssm)
res_switch.update_filter(kfilter)
# Univariate filter
mod.ssm.filter_univariate = True
res_uv = mod.ssm.filter()
else:
res_mv, res_switch, res_uv = mod
# Test attributes that are the same regardless of the univariate or
# multivariate method
assert_allclose(res_switch.llf, res_mv.llf)
assert_allclose(res_switch.llf, res_uv.llf)
assert_allclose(res_switch.scale, res_mv.scale)
assert_allclose(res_switch.scale, res_uv.scale)
attrs = ['forecasts_error_diffuse_cov', 'predicted_state',
'predicted_state_cov', 'predicted_diffuse_state_cov',
'filtered_state', 'filtered_state_cov', 'llf_obs']
for attr in attrs:
attr_mv = getattr(res_mv, attr)
attr_uv = getattr(res_uv, attr)
attr_switch = getattr(res_switch, attr)
if attr_mv is None:
continue
assert_allclose(attr_switch, attr_mv, atol=atol)
assert_allclose(attr_switch, attr_uv, atol=atol)
# Test attributes that can differ for the univariate vs multivariate method
attrs = ['forecasts_error', 'forecasts_error_cov', 'kalman_gain']
for attr in attrs:
# Test all periods against the multivariate filter, except for periods
# that were switched (it's easiest to just set those values to zero)
actual = getattr(res_switch, attr).copy()
desired = getattr(res_mv, attr).copy()
actual[..., periods] = 0
desired[..., periods] = 0
assert_allclose(actual, desired, atol=atol)
# Test switched periods against the univariate filter
actual = getattr(res_switch, attr)[..., periods]
desired = getattr(res_uv, attr)[..., periods]
assert_allclose(actual, desired, atol=atol)
def check_smoother_output(mod, periods, atol=1e-12):
if isinstance(mod, mlemodel.MLEModel):
# Multivariate filter / smoother
res_mv = mod.ssm.smooth()
# Manually perform filtering / smoothing with a switch
kfilter = mod.ssm._kalman_filter
kfilter.seek(0, True)
kfilter.univariate_filter[periods] = 1
for _ in range(mod.nobs):
next(kfilter)
# Create the results object
res_switch = mod.ssm.results_class(mod.ssm)
res_switch.update_representation(mod.ssm)
res_switch.update_filter(kfilter)
mod.ssm._kalman_smoother.reset(True)
smoother = mod.ssm._smooth()
res_switch.update_smoother(smoother)
# Univariate filter / smoother
mod.ssm.filter_univariate = True
res_uv = mod.ssm.smooth()
else:
res_mv, res_switch, res_uv = mod
# Test attributes that are the same regardless of the univariate or
# multivariate method
attrs = ['scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov',
'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov',
'smoothed_state_disturbance', 'smoothed_state_disturbance_cov',
'innovations_transition']
for attr in attrs:
attr_mv = getattr(res_mv, attr)
attr_uv = getattr(res_uv, attr)
attr_switch = getattr(res_switch, attr)
if attr_mv is None:
continue
assert_allclose(attr_uv, attr_mv, atol=atol)
assert_allclose(attr_switch, attr_mv, atol=atol)
assert_allclose(attr_switch, attr_uv, atol=atol)
# Test attributes that can differ for the univariate vs multivariate method
attrs = ['smoothing_error', 'smoothed_measurement_disturbance',
'smoothed_measurement_disturbance_cov']
for attr in attrs:
attr_mv = getattr(res_mv, attr)
attr_uv = getattr(res_uv, attr)
attr_switch = getattr(res_switch, attr)
if attr_mv is None:
continue
# Test all periods against the multivariate filter, except for periods
# that were switched (it's easiest to just set those values to zero)
actual = attr_switch.copy()
desired = attr_mv.copy()
actual[..., periods] = 0
desired[..., periods] = 0
assert_allclose(actual, desired)
@pytest.mark.parametrize('missing', [None, 'init', 'mixed', 'all'])
def test_basic(missing):
# Test that the multivariate filter switches to the univariate filter
# when it runs into problems
mod = get_model(univariate=True, missing=missing)
# Here, because of the known initialization with P_0 = [[0]], we will also
# have F_0 = 0.
# Then the Kalman filter gives P_0|0 = 0, and P_1 = Q = [[1.]]
# so that F_1 != 0, and the rest of the periods do not have a singular
# forecast error covariance matrix.
mod.initialize_known([0], [[0]])
mod.ssm.filter()
uf = np.array(mod.ssm._kalman_filter.univariate_filter)
# As a result, we expect that in the period t=0, we had to fall back to the
# univariate filter, while in the periods t >= 1, the multivariate filter
# works as usual.
# However, if the first period is missing (as in init and all), then we
# essentially skip the forecast error and forecast error cov computation.
# As a result, we don't need to switch to the univariate methods
if missing in ['init', 'all']:
assert_allclose(uf, 0)
else:
assert_allclose(uf[0], 1)
assert_allclose(uf[1:], 0)
@pytest.mark.parametrize('univariate', [True, False])
@pytest.mark.parametrize('missing', [None, 'init', 'mixed', 'all'])
@pytest.mark.parametrize(
'init', ['stationary', 'diffuse', 'approximate_diffuse'])
@pytest.mark.parametrize('periods', [np.s_[0], np.s_[4:6], np.s_[:]])
def test_filter_output(univariate, missing, init, periods):
# Test the output when the multivariate filter switches to the univariate
# filter
mod = get_model(univariate, missing, init)
check_filter_output(mod, periods, atol=1e-10 if i386_looser_tolerances else 0)
@pytest.mark.parametrize('univariate', [True, False])
@pytest.mark.parametrize('missing', [None, 'init', 'mixed', 'all'])
@pytest.mark.parametrize('init',
['stationary', 'diffuse', 'approximate_diffuse'])
@pytest.mark.parametrize('periods', [np.s_[0], np.s_[4:6], np.s_[:]])
@pytest.mark.parametrize('option', [None, 'alternate_timing'])
def test_smoother_output(univariate, missing, init, periods, option):
# Test the output when the multivariate filter switches to the univariate
# filter
mod = get_model(univariate, missing, init)
if option == 'alternate_timing':
# Can't use diffuse initialization with alternate timing
if init == 'diffuse':
return
mod.ssm.timing_init_filtered = True
atol = 1e-8 if i386_looser_tolerances else 1e-12
# Tolerance is lower for approximate diffuse for one attribute in this case
if missing == 'init' and init == 'approximate_diffuse':
atol = 1e-6
check_smoother_output(mod, periods, atol=atol)
def test_invalid_options():
mod = get_model(univariate=True)
mod.initialize_known([0], [[0]])
mod.ssm.set_inversion_method(0, solve_lu=True)
msg = ('Singular forecast error covariance matrix detected, but'
' multivariate filter cannot fall back to univariate'
' filter when the inversion method is set to anything'
' other than INVERT_UNIVARIATE or SOLVE_CHOLESKY.')
with pytest.raises(NotImplementedError, match=msg):
mod.ssm.filter()
mod = get_model(univariate=True)
mod.initialize_known([0], [[0]])
mod.ssm.smooth_classical = True
msg = ('Cannot use classical smoothing when the multivariate filter has'
' fallen back to univariate filtering.')
with pytest.raises(NotImplementedError, match=msg):
mod.ssm.smooth()
mod = get_model(univariate=True)
mod.initialize_known([0], [[0]])
mod.ssm.smooth_alternative = True
msg = ('Cannot use alternative smoothing when the multivariate filter has'
' fallen back to univariate filtering.')
with pytest.raises(NotImplementedError, match=msg):
mod.ssm.smooth()
@pytest.mark.parametrize('missing', [None, 'init', 'mixed', 'all'])
@pytest.mark.parametrize('periods', [np.s_[0], np.s_[4:6], np.s_[:]])
@pytest.mark.parametrize('use_exact_diffuse', [False, True])
def test_sarimax(missing, periods, use_exact_diffuse):
endog = np.array([0.5, 1.2, -0.2, 0.3, -0.1, 0.4, 1.4, 0.9])
exog = np.ones_like(endog)
if missing == 'init':
endog[0:2] = np.nan
elif missing == 'mixed':
endog[2:4] = np.nan
elif missing == 'all':
endog[:] = np.nan
mod = sarimax.SARIMAX(endog, order=(1, 1, 1), trend='t',
seasonal_order=(1, 1, 1, 2), exog=exog,
use_exact_diffuse=use_exact_diffuse)
mod.update([0.1, 0.3, 0.5, 0.2, 0.05, -0.1, 1.0])
check_filter_output(mod, periods, atol=1e-8)
check_smoother_output(mod, periods)
@pytest.mark.parametrize('missing', [None, 'init', 'mixed', 'all'])
@pytest.mark.parametrize('periods', [np.s_[0], np.s_[4:6], np.s_[:]])
@pytest.mark.parametrize('use_exact_diffuse', [False, True])
def test_unobserved_components(missing, periods, use_exact_diffuse):
endog = np.array([0.5, 1.2, -0.2, 0.3, -0.1, 0.4, 1.4, 0.9])
exog = np.ones_like(endog)
if missing == 'init':
endog[0:2] = np.nan
elif missing == 'mixed':
endog[2:4] = np.nan
elif missing == 'all':
endog[:] = np.nan
mod = structural.UnobservedComponents(
endog, 'llevel', exog=exog, seasonal=2, autoregressive=1,
use_exact_diffuse=use_exact_diffuse)
mod.update([1.0, 0.1, 0.3, 0.05, 0.15, 0.5])
check_filter_output(mod, periods)
check_smoother_output(mod, periods)
@pytest.mark.parametrize('missing', [None, 'init', 'mixed', 'all'])
@pytest.mark.parametrize('periods', [np.s_[0], np.s_[4:6], np.s_[:]])
def test_varmax(missing, periods):
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
exog = np.ones_like(endog[:, 0])
if missing == 'init':
endog[0:2, :] = np.nan
elif missing == 'mixed':
endog[2:4, 0] = np.nan
endog[3:6, 1] = np.nan
elif missing == 'all':
endog[:] = np.nan
mod = varmax.VARMAX(endog, order=(1, 0), trend='t', exog=exog)
mod.update([0.1, -0.1, 0.5, 0.1, -0.05, 0.2, 0.4, 0.25, 1.2, 0.4, 2.3])
check_filter_output(mod, periods, atol=1e-12)
check_smoother_output(mod, periods)
@pytest.mark.parametrize('missing', [None, 'init', 'mixed', 'all'])
@pytest.mark.parametrize('periods', [np.s_[0], np.s_[4:6], np.s_[:]])
def test_dynamic_factor(missing, periods):
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
exog = np.ones_like(endog[:, 0])
if missing == 'init':
endog[0:2, :] = np.nan
elif missing == 'mixed':
endog[2:4, 0] = np.nan
endog[3:6, 1] = np.nan
elif missing == 'all':
endog[:] = np.nan
mod = dynamic_factor.DynamicFactor(endog, k_factors=1, factor_order=2,
exog=exog)
mod.update([1.0, -0.5, 0.3, -0.1, 1.2, 2.3, 0.5, 0.1])
check_filter_output(mod, periods)
check_smoother_output(mod, periods)
@pytest.mark.parametrize('missing', [None, 'mixed'])
def test_simulation_smoothing(missing):
# Test that the simulation smoother works when the multivariate filter
# switches to the univariate filter when it runs into problems
# (see test_basic for a description of the model used here)
# Get the model where switching will occur
mod_switch = get_model(univariate=True, missing=missing)
mod_switch.initialize_known([0], [[0]])
sim_switch = mod_switch.simulation_smoother()
# Get the model where we have specified univariate filtering (so there is
# no need to switch)
mod_uv = get_model(univariate=True, missing=missing)
mod_uv.initialize_known([0], [[0]])
mod_uv.ssm.filter_univariate = True
sim_uv = mod_uv.simulation_smoother()
# Test for basic simulationg of a new observed series
np.random.seed(1234)
simulate_switch = mod_switch.simulate([], 10)
np.random.seed(1234)
simulate_uv = mod_uv.simulate([], 10)
assert_allclose(simulate_switch, simulate_uv)
# Perform simulation smoothing
np.random.seed(1234)
sim_switch.simulate()
np.random.seed(1234)
sim_uv.simulate()
# Make sure that switching happened in the first model but not the second
kfilter = sim_switch._simulation_smoother.simulated_kfilter
uf_switch = np.array(kfilter.univariate_filter, copy=True)
assert_allclose(uf_switch[0], 1)
assert_allclose(uf_switch[1:], 0)
kfilter = sim_uv._simulation_smoother.simulated_kfilter.univariate_filter
uf_uv = np.array(kfilter, copy=True)
assert_allclose(uf_uv, 1)
if missing == 'mixed':
kfilter = (sim_switch._simulation_smoother
.secondary_simulated_kfilter.univariate_filter)
uf_switch = np.array(kfilter, copy=True)
assert_allclose(uf_switch[0], 1)
assert_allclose(uf_switch[1:], 0)
kfilter = (sim_uv._simulation_smoother
.secondary_simulated_kfilter.univariate_filter)
uf_uv = np.array(kfilter, copy=True)
assert_allclose(uf_uv, 1)
# Test all simulation smoothing output
attrs = ['generated_measurement_disturbance',
'generated_state_disturbance', 'generated_obs', 'generated_state',
'simulated_state', 'simulated_measurement_disturbance',
'simulated_state_disturbance']
for attr in attrs:
assert_allclose(getattr(sim_switch, attr), getattr(sim_uv, attr))
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])
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