r""" Tests for smoothing and estimation of unobserved states and disturbances - Predicted states: :math:`E(\alpha_t | Y_{t-1})` - Filtered states: :math:`E(\alpha_t | Y_t)` - Smoothed states: :math:`E(\alpha_t | Y_n)` - Smoothed disturbances :math:`E(\varepsilon_t | Y_n), E(\eta_t | Y_n)` Tested against R (FKF, KalmanRun / KalmanSmooth), Stata (sspace), and MATLAB (ssm toolbox) Author: Chad Fulton License: Simplified-BSD """ import os import numpy as np from numpy.testing import assert_allclose, assert_almost_equal, assert_equal import pandas as pd import pytest from statsmodels import datasets from statsmodels.tsa.statespace import mlemodel, sarimax, varmax from statsmodels.tsa.statespace.tests.test_impulse_responses import TVSS from statsmodels.tsa.statespace.kalman_filter import FILTER_UNIVARIATE from statsmodels.tsa.statespace.kalman_smoother import ( SMOOTH_CLASSICAL, SMOOTH_ALTERNATIVE, SMOOTH_UNIVARIATE) current_path = os.path.dirname(os.path.abspath(__file__)) class TestStatesAR3: @classmethod def setup_class(cls, alternate_timing=False, *args, **kwargs): # Dataset / Stata comparison path = os.path.join(current_path, 'results', 'results_wpi1_ar3_stata.csv') cls.stata = pd.read_csv(path) cls.stata.index = pd.date_range(start='1960-01-01', periods=124, freq='QS') # Matlab comparison path = os.path.join(current_path, 'results', 'results_wpi1_ar3_matlab_ssm.csv') matlab_names = [ 'a1', 'a2', 'a3', 'detP', 'alphahat1', 'alphahat2', 'alphahat3', 'detV', 'eps', 'epsvar', 'eta', 'etavar' ] cls.matlab_ssm = pd.read_csv(path, header=None, names=matlab_names) cls.model = sarimax.SARIMAX( cls.stata['wpi'], order=(3, 1, 0), simple_differencing=True, hamilton_representation=True, *args, **kwargs ) if alternate_timing: cls.model.ssm.timing_init_filtered = True # Parameters from from Stata's sspace MLE estimation params = np.r_[.5270715, .0952613, .2580355, .5307459] cls.results = cls.model.smooth(params, cov_type='none') # Calculate the determinant of the covariance matrices (for easy # comparison to other languages without having to store 2-dim arrays) cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs)) for i in range(cls.model.nobs): cls.results.det_predicted_state_cov[0, i] = np.linalg.det( cls.results.filter_results.predicted_state_cov[:, :, i]) cls.results.det_smoothed_state_cov[0, i] = np.linalg.det( cls.results.smoother_results.smoothed_state_cov[:, :, i]) # Perform simulation smoothing nobs = cls.model.nobs k_endog = cls.model.k_endog k_posdef = cls.model.ssm.k_posdef cls.sim = cls.model.simulation_smoother(filter_timing=0) cls.sim.simulate( measurement_disturbance_variates=np.zeros(nobs * k_endog), state_disturbance_variates=np.zeros(nobs * k_posdef), initial_state_variates=np.zeros(cls.model.k_states) ) def test_predict_obs(self): assert_almost_equal( self.results.filter_results.predict().forecasts[0], self.stata.iloc[1:]['dep1'], 4 ) def test_standardized_residuals(self): assert_almost_equal( self.results.filter_results.standardized_forecasts_error[0], self.stata.iloc[1:]['sr1'], 4 ) def test_predicted_states(self): assert_almost_equal( self.results.filter_results.predicted_state[:, :-1].T, self.stata.iloc[1:][['sp1', 'sp2', 'sp3']], 4 ) assert_almost_equal( self.results.filter_results.predicted_state[:, :-1].T, self.matlab_ssm[['a1', 'a2', 'a3']], 4 ) def test_predicted_states_cov(self): assert_almost_equal( self.results.det_predicted_state_cov.T, self.matlab_ssm[['detP']], 4 ) def test_filtered_states(self): assert_almost_equal( self.results.filter_results.filtered_state.T, self.stata.iloc[1:][['sf1', 'sf2', 'sf3']], 4 ) def test_smoothed_states(self): assert_almost_equal( self.results.smoother_results.smoothed_state.T, self.stata.iloc[1:][['sm1', 'sm2', 'sm3']], 4 ) assert_almost_equal( self.results.smoother_results.smoothed_state.T, self.matlab_ssm[['alphahat1', 'alphahat2', 'alphahat3']], 4 ) def test_smoothed_states_cov(self): assert_almost_equal( self.results.det_smoothed_state_cov.T, self.matlab_ssm[['detV']], 4 ) def test_smoothed_measurement_disturbance(self): assert_almost_equal( self.results.smoother_results.smoothed_measurement_disturbance.T, self.matlab_ssm[['eps']], 4 ) def test_smoothed_measurement_disturbance_cov(self): res = self.results.smoother_results assert_almost_equal( res.smoothed_measurement_disturbance_cov[0].T, self.matlab_ssm[['epsvar']], 4 ) def test_smoothed_state_disturbance(self): assert_almost_equal( self.results.smoother_results.smoothed_state_disturbance.T, self.matlab_ssm[['eta']], 4 ) def test_smoothed_state_disturbance_cov(self): assert_almost_equal( self.results.smoother_results.smoothed_state_disturbance_cov[0].T, self.matlab_ssm[['etavar']], 4 ) class TestStatesAR3AlternateTiming(TestStatesAR3): @classmethod def setup_class(cls, *args, **kwargs): super().setup_class( alternate_timing=True, *args, **kwargs) class TestStatesAR3AlternativeSmoothing(TestStatesAR3): @classmethod def setup_class(cls, *args, **kwargs): super().setup_class( smooth_method=SMOOTH_ALTERNATIVE, *args, **kwargs) def test_smoothed_states(self): # Initialization issues can change the first few smoothed states assert_almost_equal( self.results.smoother_results.smoothed_state.T[2:], self.stata.iloc[3:][['sm1', 'sm2', 'sm3']], 4 ) assert_almost_equal( self.results.smoother_results.smoothed_state.T[2:], self.matlab_ssm.iloc[2:][['alphahat1', 'alphahat2', 'alphahat3']], 4 ) def test_smoothed_states_cov(self): assert_almost_equal( self.results.det_smoothed_state_cov.T[1:], self.matlab_ssm.iloc[1:][['detV']], 4 ) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_ALTERNATIVE) class TestStatesAR3UnivariateSmoothing(TestStatesAR3): @classmethod def setup_class(cls, *args, **kwargs): super().setup_class( filter_method=FILTER_UNIVARIATE, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_UNIVARIATE) class TestStatesMissingAR3: @classmethod def setup_class(cls, alternate_timing=False, *args, **kwargs): # Dataset path = os.path.join(current_path, 'results', 'results_wpi1_ar3_stata.csv') cls.stata = pd.read_csv(path) cls.stata.index = pd.date_range(start='1960-01-01', periods=124, freq='QS') # Matlab comparison path = os.path.join(current_path, 'results', 'results_wpi1_missing_ar3_matlab_ssm.csv') matlab_names = [ 'a1', 'a2', 'a3', 'detP', 'alphahat1', 'alphahat2', 'alphahat3', 'detV', 'eps', 'epsvar', 'eta', 'etavar' ] cls.matlab_ssm = pd.read_csv(path, header=None, names=matlab_names) # KFAS comparison path = os.path.join(current_path, 'results', 'results_smoothing3_R.csv') cls.R_ssm = pd.read_csv(path) # Create missing observations cls.stata['dwpi'] = cls.stata['wpi'].diff() cls.stata.loc[cls.stata.index[10:21], 'dwpi'] = np.nan cls.model = sarimax.SARIMAX( cls.stata.loc[cls.stata.index[1:], 'dwpi'], order=(3, 0, 0), hamilton_representation=True, *args, **kwargs ) if alternate_timing: cls.model.ssm.timing_init_filtered = True # Parameters from from Stata's sspace MLE estimation params = np.r_[.5270715, .0952613, .2580355, .5307459] cls.results = cls.model.smooth(params, return_ssm=True) # Calculate the determinant of the covariance matrices (for easy # comparison to other languages without having to store 2-dim arrays) cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs)) for i in range(cls.model.nobs): cls.results.det_predicted_state_cov[0, i] = np.linalg.det( cls.results.predicted_state_cov[:, :, i]) cls.results.det_smoothed_state_cov[0, i] = np.linalg.det( cls.results.smoothed_state_cov[:, :, i]) # Perform simulation smoothing nobs = cls.model.nobs k_endog = cls.model.k_endog k_posdef = cls.model.ssm.k_posdef cls.sim = cls.model.simulation_smoother() cls.sim.simulate( measurement_disturbance_variates=np.zeros(nobs * k_endog), state_disturbance_variates=np.zeros(nobs * k_posdef), initial_state_variates=np.zeros(cls.model.k_states) ) def test_predicted_states(self): assert_almost_equal( self.results.predicted_state[:, :-1].T, self.matlab_ssm[['a1', 'a2', 'a3']], 4 ) def test_predicted_states_cov(self): assert_almost_equal( self.results.det_predicted_state_cov.T, self.matlab_ssm[['detP']], 4 ) def test_smoothed_states(self): assert_almost_equal( self.results.smoothed_state.T, self.matlab_ssm[['alphahat1', 'alphahat2', 'alphahat3']], 4 ) def test_smoothed_states_cov(self): assert_almost_equal( self.results.det_smoothed_state_cov.T, self.matlab_ssm[['detV']], 4 ) def test_smoothed_measurement_disturbance(self): assert_almost_equal( self.results.smoothed_measurement_disturbance.T, self.matlab_ssm[['eps']], 4 ) def test_smoothed_measurement_disturbance_cov(self): assert_almost_equal( self.results.smoothed_measurement_disturbance_cov[0].T, self.matlab_ssm[['epsvar']], 4 ) # There is a discrepancy between MATLAB ssm toolbox and # statsmodels.tsa.statespace on the following variables in the case of # missing data. Tests against the R package KFAS confirm our results def test_smoothed_state_disturbance(self): # See note above about why this assertion is invalid # assert_almost_equal( # self.results.smoothed_state_disturbance.T, # self.matlab_ssm[['eta']], 4 # ) assert_almost_equal( self.results.smoothed_state_disturbance.T, self.R_ssm[['etahat']], 9 ) def test_smoothed_state_disturbance_cov(self): # See note above about why this assertion is invalid # assert_almost_equal( # self.results.smoothed_state_disturbance_cov[0].T, # self.matlab_ssm[['etavar']], 4 # ) assert_almost_equal( self.results.smoothed_state_disturbance_cov[0, 0, :], self.R_ssm['detVeta'], 9 ) class TestStatesMissingAR3AlternateTiming(TestStatesMissingAR3): @classmethod def setup_class(cls, *args, **kwargs): super().setup_class(alternate_timing=True, *args, **kwargs) class TestStatesMissingAR3AlternativeSmoothing(TestStatesMissingAR3): @classmethod def setup_class(cls, *args, **kwargs): super().setup_class( smooth_method=SMOOTH_ALTERNATIVE, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_ALTERNATIVE) class TestStatesMissingAR3UnivariateSmoothing(TestStatesMissingAR3): @classmethod def setup_class(cls, *args, **kwargs): super().setup_class( filter_method=FILTER_UNIVARIATE, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_UNIVARIATE) class TestMultivariateMissing: """ Tests for most filtering and smoothing variables against output from the R library KFAS. Note that KFAS uses the univariate approach which generally will result in different predicted values and covariance matrices associated with the measurement equation (e.g. forecasts, etc.). In this case, although the model is multivariate, each of the series is truly independent so the values will be the same regardless of whether the univariate approach is used or not. """ @classmethod def setup_class(cls, **kwargs): # Results path = os.path.join(current_path, 'results', 'results_smoothing_R.csv') cls.desired = pd.read_csv(path) # Data dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') obs = dta[['realgdp', 'realcons', 'realinv']].diff().iloc[1:] obs.iloc[0:50, 0] = np.nan obs.iloc[19:70, 1] = np.nan obs.iloc[39:90, 2] = np.nan obs.iloc[119:130, 0] = np.nan obs.iloc[119:130, 2] = np.nan # Create the model mod = mlemodel.MLEModel(obs, k_states=3, k_posdef=3, **kwargs) mod['design'] = np.eye(3) mod['obs_cov'] = np.eye(3) mod['transition'] = np.eye(3) mod['selection'] = np.eye(3) mod['state_cov'] = np.eye(3) mod.initialize_approximate_diffuse(1e6) cls.model = mod cls.results = mod.smooth([], return_ssm=True) # Calculate the determinant of the covariance matrices (for easy # comparison to other languages without having to store 2-dim arrays) cls.results.det_scaled_smoothed_estimator_cov = ( np.zeros((1, cls.model.nobs))) cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_disturbance_cov = ( np.zeros((1, cls.model.nobs))) for i in range(cls.model.nobs): cls.results.det_scaled_smoothed_estimator_cov[0, i] = ( np.linalg.det( cls.results.scaled_smoothed_estimator_cov[:, :, i])) cls.results.det_predicted_state_cov[0, i] = np.linalg.det( cls.results.predicted_state_cov[:, :, i+1]) cls.results.det_smoothed_state_cov[0, i] = np.linalg.det( cls.results.smoothed_state_cov[:, :, i]) cls.results.det_smoothed_state_disturbance_cov[0, i] = ( np.linalg.det( cls.results.smoothed_state_disturbance_cov[:, :, i])) def test_loglike(self): assert_allclose(np.sum(self.results.llf_obs), -205310.9767) def test_scaled_smoothed_estimator(self): assert_allclose( self.results.scaled_smoothed_estimator.T, self.desired[['r1', 'r2', 'r3']] ) def test_scaled_smoothed_estimator_cov(self): assert_allclose( self.results.det_scaled_smoothed_estimator_cov.T, self.desired[['detN']] ) def test_forecasts(self): assert_allclose( self.results.forecasts.T, self.desired[['m1', 'm2', 'm3']] ) def test_forecasts_error(self): assert_allclose( self.results.forecasts_error.T, self.desired[['v1', 'v2', 'v3']] ) def test_forecasts_error_cov(self): assert_allclose( self.results.forecasts_error_cov.diagonal(), self.desired[['F1', 'F2', 'F3']] ) def test_predicted_states(self): assert_allclose( self.results.predicted_state[:, 1:].T, self.desired[['a1', 'a2', 'a3']] ) def test_predicted_states_cov(self): assert_allclose( self.results.det_predicted_state_cov.T, self.desired[['detP']] ) def test_smoothed_states(self): assert_allclose( self.results.smoothed_state.T, self.desired[['alphahat1', 'alphahat2', 'alphahat3']] ) def test_smoothed_states_cov(self): assert_allclose( self.results.det_smoothed_state_cov.T, self.desired[['detV']] ) def test_smoothed_forecasts(self): assert_allclose( self.results.smoothed_forecasts.T, self.desired[['muhat1', 'muhat2', 'muhat3']] ) def test_smoothed_state_disturbance(self): assert_allclose( self.results.smoothed_state_disturbance.T, self.desired[['etahat1', 'etahat2', 'etahat3']] ) def test_smoothed_state_disturbance_cov(self): assert_allclose( self.results.det_smoothed_state_disturbance_cov.T, self.desired[['detVeta']] ) def test_smoothed_measurement_disturbance(self): assert_allclose( self.results.smoothed_measurement_disturbance.T, self.desired[['epshat1', 'epshat2', 'epshat3']] ) def test_smoothed_measurement_disturbance_cov(self): assert_allclose( self.results.smoothed_measurement_disturbance_cov.diagonal(), self.desired[['Veps1', 'Veps2', 'Veps3']] ) class TestMultivariateMissingClassicalSmoothing(TestMultivariateMissing): @classmethod def setup_class(cls, *args, **kwargs): super().setup_class( smooth_method=SMOOTH_CLASSICAL, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, SMOOTH_CLASSICAL) assert_equal(self.model.ssm._kalman_smoother.smooth_method, SMOOTH_CLASSICAL) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_CLASSICAL) class TestMultivariateMissingAlternativeSmoothing(TestMultivariateMissing): @classmethod def setup_class(cls, *args, **kwargs): super().setup_class( smooth_method=SMOOTH_ALTERNATIVE, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_ALTERNATIVE) class TestMultivariateMissingUnivariateSmoothing(TestMultivariateMissing): @classmethod def setup_class(cls, *args, **kwargs): super().setup_class( filter_method=FILTER_UNIVARIATE, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_UNIVARIATE) class TestMultivariateVAR: """ Tests for most filtering and smoothing variables against output from the R library KFAS. Note that KFAS uses the univariate approach which generally will result in different predicted values and covariance matrices associated with the measurement equation (e.g. forecasts, etc.). In this case, although the model is multivariate, each of the series is truly independent so the values will be the same regardless of whether the univariate approach is used or not. """ @classmethod def setup_class(cls, *args, **kwargs): # Results path = os.path.join(current_path, 'results', 'results_smoothing2_R.csv') cls.desired = pd.read_csv(path) # Data dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') obs = np.log(dta[['realgdp', 'realcons', 'realinv']]).diff().iloc[1:] # Create the model mod = mlemodel.MLEModel(obs, k_states=3, k_posdef=3, **kwargs) mod['design'] = np.eye(3) mod['obs_cov'] = np.array([ [0.0000640649, 0., 0.], [0., 0.0000572802, 0.], [0., 0., 0.0017088585]]) mod['transition'] = np.array([ [-0.1119908792, 0.8441841604, 0.0238725303], [0.2629347724, 0.4996718412, -0.0173023305], [-3.2192369082, 4.1536028244, 0.4514379215]]) mod['selection'] = np.eye(3) mod['state_cov'] = np.array([ [0.0000640649, 0.0000388496, 0.0002148769], [0.0000388496, 0.0000572802, 0.000001555], [0.0002148769, 0.000001555, 0.0017088585]]) mod.initialize_approximate_diffuse(1e6) cls.model = mod cls.results = mod.smooth([], return_ssm=True) # Calculate the determinant of the covariance matrices (for easy # comparison to other languages without having to store 2-dim arrays) cls.results.det_scaled_smoothed_estimator_cov = ( np.zeros((1, cls.model.nobs))) cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_disturbance_cov = ( np.zeros((1, cls.model.nobs))) for i in range(cls.model.nobs): cls.results.det_scaled_smoothed_estimator_cov[0, i] = ( np.linalg.det( cls.results.scaled_smoothed_estimator_cov[:, :, i])) cls.results.det_predicted_state_cov[0, i] = np.linalg.det( cls.results.predicted_state_cov[:, :, i+1]) cls.results.det_smoothed_state_cov[0, i] = np.linalg.det( cls.results.smoothed_state_cov[:, :, i]) cls.results.det_smoothed_state_disturbance_cov[0, i] = ( np.linalg.det( cls.results.smoothed_state_disturbance_cov[:, :, i])) def test_loglike(self): assert_allclose(np.sum(self.results.llf_obs), 1695.34872) def test_scaled_smoothed_estimator(self): assert_allclose( self.results.scaled_smoothed_estimator.T, self.desired[['r1', 'r2', 'r3']], atol=1e-4 ) def test_scaled_smoothed_estimator_cov(self): # Last obs is zero, so exclude it assert_allclose( np.log(self.results.det_scaled_smoothed_estimator_cov.T[:-1]), np.log(self.desired[['detN']][:-1]), atol=1e-6 ) def test_forecasts(self): assert_allclose( self.results.forecasts.T, self.desired[['m1', 'm2', 'm3']], atol=1e-6 ) def test_forecasts_error(self): assert_allclose( self.results.forecasts_error.T[:, 0], self.desired['v1'], atol=1e-6 ) def test_forecasts_error_cov(self): assert_allclose( self.results.forecasts_error_cov.diagonal()[:, 0], self.desired['F1'], atol=1e-6 ) def test_predicted_states(self): assert_allclose( self.results.predicted_state[:, 1:].T, self.desired[['a1', 'a2', 'a3']], atol=1e-6 ) def test_predicted_states_cov(self): assert_allclose( self.results.det_predicted_state_cov.T, self.desired[['detP']], atol=1e-16 ) def test_smoothed_states(self): assert_allclose( self.results.smoothed_state.T, self.desired[['alphahat1', 'alphahat2', 'alphahat3']], atol=1e-6 ) def test_smoothed_states_cov(self): assert_allclose( self.results.det_smoothed_state_cov.T, self.desired[['detV']], atol=1e-16 ) def test_smoothed_forecasts(self): assert_allclose( self.results.smoothed_forecasts.T, self.desired[['muhat1', 'muhat2', 'muhat3']], atol=1e-6 ) def test_smoothed_state_disturbance(self): assert_allclose( self.results.smoothed_state_disturbance.T, self.desired[['etahat1', 'etahat2', 'etahat3']], atol=1e-6 ) def test_smoothed_state_disturbance_cov(self): assert_allclose( self.results.det_smoothed_state_disturbance_cov.T, self.desired[['detVeta']], atol=1e-18 ) def test_smoothed_measurement_disturbance(self): assert_allclose( self.results.smoothed_measurement_disturbance.T, self.desired[['epshat1', 'epshat2', 'epshat3']], atol=1e-6 ) def test_smoothed_measurement_disturbance_cov(self): assert_allclose( self.results.smoothed_measurement_disturbance_cov.diagonal(), self.desired[['Veps1', 'Veps2', 'Veps3']], atol=1e-6 ) class TestMultivariateVARAlternativeSmoothing(TestMultivariateVAR): @classmethod def setup_class(cls, *args, **kwargs): super().setup_class( smooth_method=SMOOTH_ALTERNATIVE, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_ALTERNATIVE) class TestMultivariateVARClassicalSmoothing(TestMultivariateVAR): @classmethod def setup_class(cls, *args, **kwargs): super().setup_class( smooth_method=SMOOTH_CLASSICAL, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, SMOOTH_CLASSICAL) assert_equal(self.model.ssm._kalman_smoother.smooth_method, SMOOTH_CLASSICAL) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_CLASSICAL) class TestMultivariateVARUnivariate: """ Tests for most filtering and smoothing variables against output from the R library KFAS. Note that KFAS uses the univariate approach which generally will result in different predicted values and covariance matrices associated with the measurement equation (e.g. forecasts, etc.). In this case, although the model is multivariate, each of the series is truly independent so the values will be the same regardless of whether the univariate approach is used or not. """ @classmethod def setup_class(cls, *args, **kwargs): # Results path = os.path.join(current_path, 'results', 'results_smoothing2_R.csv') cls.desired = pd.read_csv(path) # Data dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') obs = np.log(dta[['realgdp', 'realcons', 'realinv']]).diff().iloc[1:] # Create the model mod = mlemodel.MLEModel(obs, k_states=3, k_posdef=3, **kwargs) mod.ssm.filter_univariate = True mod['design'] = np.eye(3) mod['obs_cov'] = np.array([ [0.0000640649, 0., 0.], [0., 0.0000572802, 0.], [0., 0., 0.0017088585]]) mod['transition'] = np.array([ [-0.1119908792, 0.8441841604, 0.0238725303], [0.2629347724, 0.4996718412, -0.0173023305], [-3.2192369082, 4.1536028244, 0.4514379215]]) mod['selection'] = np.eye(3) mod['state_cov'] = np.array([ [0.0000640649, 0.0000388496, 0.0002148769], [0.0000388496, 0.0000572802, 0.000001555], [0.0002148769, 0.000001555, 0.0017088585]]) mod.initialize_approximate_diffuse(1e6) cls.model = mod cls.results = mod.smooth([], return_ssm=True) # Calculate the determinant of the covariance matrices (for easy # comparison to other languages without having to store 2-dim arrays) cls.results.det_scaled_smoothed_estimator_cov = ( np.zeros((1, cls.model.nobs))) cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_disturbance_cov = ( np.zeros((1, cls.model.nobs))) for i in range(cls.model.nobs): cls.results.det_scaled_smoothed_estimator_cov[0, i] = ( np.linalg.det( cls.results.scaled_smoothed_estimator_cov[:, :, i])) cls.results.det_predicted_state_cov[0, i] = np.linalg.det( cls.results.predicted_state_cov[:, :, i+1]) cls.results.det_smoothed_state_cov[0, i] = np.linalg.det( cls.results.smoothed_state_cov[:, :, i]) cls.results.det_smoothed_state_disturbance_cov[0, i] = ( np.linalg.det( cls.results.smoothed_state_disturbance_cov[:, :, i])) def test_loglike(self): assert_allclose(np.sum(self.results.llf_obs), 1695.34872) def test_scaled_smoothed_estimator(self): assert_allclose( self.results.scaled_smoothed_estimator.T, self.desired[['r1', 'r2', 'r3']], atol=1e-4 ) def test_scaled_smoothed_estimator_cov(self): # Last obs is zero, so exclude it assert_allclose( np.log(self.results.det_scaled_smoothed_estimator_cov.T[:-1]), np.log(self.desired[['detN']][:-1]) ) def test_forecasts(self): assert_allclose( self.results.forecasts.T[:, 0], self.desired['m1'], atol=1e-6 ) def test_forecasts_error(self): assert_allclose( self.results.forecasts_error.T, self.desired[['v1', 'v2', 'v3']], atol=1e-6 ) def test_forecasts_error_cov(self): assert_allclose( self.results.forecasts_error_cov.diagonal(), self.desired[['F1', 'F2', 'F3']] ) def test_predicted_states(self): assert_allclose( self.results.predicted_state[:, 1:].T, self.desired[['a1', 'a2', 'a3']], atol=1e-8 ) def test_predicted_states_cov(self): assert_allclose( self.results.det_predicted_state_cov.T, self.desired[['detP']], atol=1e-18 ) def test_smoothed_states(self): assert_allclose( self.results.smoothed_state.T, self.desired[['alphahat1', 'alphahat2', 'alphahat3']], atol=1e-6 ) def test_smoothed_states_cov(self): assert_allclose( self.results.det_smoothed_state_cov.T, self.desired[['detV']], atol=1e-18 ) def test_smoothed_forecasts(self): assert_allclose( self.results.smoothed_forecasts.T, self.desired[['muhat1', 'muhat2', 'muhat3']], atol=1e-6 ) def test_smoothed_state_disturbance(self): assert_allclose( self.results.smoothed_state_disturbance.T, self.desired[['etahat1', 'etahat2', 'etahat3']], atol=1e-6 ) def test_smoothed_state_disturbance_cov(self): assert_allclose( self.results.det_smoothed_state_disturbance_cov.T, self.desired[['detVeta']], atol=1e-18 ) def test_smoothed_measurement_disturbance(self): assert_allclose( self.results.smoothed_measurement_disturbance.T, self.desired[['epshat1', 'epshat2', 'epshat3']], atol=1e-6 ) def test_smoothed_measurement_disturbance_cov(self): assert_allclose( self.results.smoothed_measurement_disturbance_cov.diagonal(), self.desired[['Veps1', 'Veps2', 'Veps3']] ) class TestMultivariateVARUnivariateSmoothing(TestMultivariateVARUnivariate): @classmethod def setup_class(cls, *args, **kwargs): super().setup_class( filter_method=FILTER_UNIVARIATE, *args, **kwargs) def test_filter_method(self): assert_equal(self.model.ssm.filter_method, FILTER_UNIVARIATE) assert_equal(self.model.ssm._kalman_smoother.filter_method, FILTER_UNIVARIATE) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_UNIVARIATE) class TestVARAutocovariances: @classmethod def setup_class(cls, which='mixed', *args, **kwargs): # Data dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') obs = np.log(dta[['realgdp', 'realcons', 'realinv']]).diff().iloc[1:] if which == 'all': obs.iloc[:50, :] = np.nan obs.iloc[119:130, :] = np.nan elif which == 'partial': obs.iloc[0:50, 0] = np.nan obs.iloc[119:130, 0] = np.nan elif which == 'mixed': obs.iloc[0:50, 0] = np.nan obs.iloc[19:70, 1] = np.nan obs.iloc[39:90, 2] = np.nan obs.iloc[119:130, 0] = np.nan obs.iloc[119:130, 2] = np.nan # Create the model with typical state space mod = mlemodel.MLEModel(obs, k_states=3, k_posdef=3, **kwargs) mod['design'] = np.eye(3) mod['obs_cov'] = np.array([ [609.0746647855, 0., 0.], [0., 1.8774916622, 0.], [0., 0., 124.6768281675]]) mod['transition'] = np.array([ [-0.8110473405, 1.8005304445, 1.0215975772], [-1.9846632699, 2.4091302213, 1.9264449765], [0.9181658823, -0.2442384581, -0.6393462272]]) mod['selection'] = np.eye(3) mod['state_cov'] = np.array([ [1552.9758843938, 612.7185121905, 877.6157204992], [612.7185121905, 467.8739411204, 70.608037339], [877.6157204992, 70.608037339, 900.5440385836]]) mod.initialize_approximate_diffuse(1e6) cls.model = mod cls.results = mod.smooth([], return_ssm=True) # Create the model with augmented state space kwargs.pop('filter_collapsed', None) mod = mlemodel.MLEModel(obs, k_states=6, k_posdef=3, **kwargs) mod['design', :3, :3] = np.eye(3) mod['obs_cov'] = np.array([ [609.0746647855, 0., 0.], [0., 1.8774916622, 0.], [0., 0., 124.6768281675]]) mod['transition', :3, :3] = np.array([ [-0.8110473405, 1.8005304445, 1.0215975772], [-1.9846632699, 2.4091302213, 1.9264449765], [0.9181658823, -0.2442384581, -0.6393462272]]) mod['transition', 3:, :3] = np.eye(3) mod['selection', :3, :3] = np.eye(3) mod['state_cov'] = np.array([ [1552.9758843938, 612.7185121905, 877.6157204992], [612.7185121905, 467.8739411204, 70.608037339], [877.6157204992, 70.608037339, 900.5440385836]]) mod.initialize_approximate_diffuse(1e6) cls.augmented_model = mod cls.augmented_results = mod.smooth([], return_ssm=True) def test_smoothed_state_autocov(self): # Cov(\alpha_{t+1}, \alpha_t) # Initialization makes these two methods slightly different for the # first few observations assert_allclose(self.results.smoothed_state_autocov[:, :, 0:5], self.augmented_results.smoothed_state_cov[:3, 3:, 1:6], atol=1e-4) assert_allclose(self.results.smoothed_state_autocov[:, :, 5:-1], self.augmented_results.smoothed_state_cov[:3, 3:, 6:], atol=1e-7) class TestVARAutocovariancesAlternativeSmoothing(TestVARAutocovariances): @classmethod def setup_class(cls, *args, **kwargs): super().setup_class( smooth_method=SMOOTH_ALTERNATIVE, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_ALTERNATIVE) class TestVARAutocovariancesClassicalSmoothing(TestVARAutocovariances): @classmethod def setup_class(cls, *args, **kwargs): super().setup_class( smooth_method=SMOOTH_CLASSICAL, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, SMOOTH_CLASSICAL) assert_equal(self.model.ssm._kalman_smoother.smooth_method, SMOOTH_CLASSICAL) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_CLASSICAL) class TestVARAutocovariancesUnivariateSmoothing(TestVARAutocovariances): @classmethod def setup_class(cls, *args, **kwargs): super().setup_class( filter_method=FILTER_UNIVARIATE, *args, **kwargs) def test_filter_method(self): assert_equal(self.model.ssm.filter_method, FILTER_UNIVARIATE) assert_equal(self.model.ssm._kalman_smoother.filter_method, FILTER_UNIVARIATE) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_UNIVARIATE) class TVSSWithLags(TVSS): def __init__(self, endog): # TVSS has 2 states, here we will add in 3 lags of those super().__init__(endog, _k_states=8) self['transition', 2:, :6] = np.eye(6)[..., None] # Can't use exact diffuse filtering self.ssm.initialize_approximate_diffuse(1e-4) def get_acov_model(missing, filter_univariate, tvp, oos=None, params=None, return_ssm=True): dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') endog = np.log(dta[['realgdp', 'realcons']]).diff().iloc[1:] if missing == 'all': endog.iloc[:5, :] = np.nan endog.iloc[11:13, :] = np.nan elif missing == 'partial': endog.iloc[0:5, 0] = np.nan endog.iloc[11:13, 0] = np.nan elif missing == 'mixed': endog.iloc[0:5, 0] = np.nan endog.iloc[1:7, 1] = np.nan endog.iloc[11:13, 0] = np.nan if oos is not None: new_ix = pd.date_range(start=endog.index[0], periods=len(endog) + oos, freq='QS') endog = endog.reindex(new_ix) if not tvp: mod = varmax.VARMAX(endog, order=(4, 0, 0), measurement_error=True, tolerance=0) mod.ssm.filter_univariate = filter_univariate if params is None: params = mod.start_params res = mod.smooth(params, return_ssm=return_ssm) else: mod = TVSSWithLags(endog) mod.ssm.filter_univariate = filter_univariate res = mod.smooth([], return_ssm=return_ssm) return mod, res @pytest.mark.parametrize('missing', ['all', 'partial', 'mixed', None]) @pytest.mark.parametrize('filter_univariate', [True, False]) @pytest.mark.parametrize('tvp', [True, False]) def test_smoothed_state_autocovariances_backwards(missing, filter_univariate, tvp): r""" Test for Cov(t, t - lag) """ _, res = get_acov_model(missing, filter_univariate, tvp) cov = res.smoothed_state_cov.transpose(2, 0, 1) desired_acov1 = cov[:, :2, 2:4] desired_acov2 = cov[:, :2, 4:6] desired_acov3 = cov[:, :2, 6:8] # Test all "backward" autocovariances: Cov(t, t-lag) acov1 = res.smoothed_state_autocovariance(1).transpose(2, 0, 1) assert_allclose(acov1[1:, :2, :2], desired_acov1[1:], rtol=1e-6, atol=1e-6) assert_equal(acov1[:1], np.nan) acov2 = res.smoothed_state_autocovariance(2).transpose(2, 0, 1) assert_allclose(acov2[2:, :2, :2], desired_acov2[2:], rtol=1e-6, atol=1e-6) assert_equal(acov2[:2], np.nan) acov3 = res.smoothed_state_autocovariance(3).transpose(2, 0, 1) assert_allclose(acov3[3:, :2, :2], desired_acov3[3:], rtol=1e-6, atol=1e-6) assert_equal(acov3[:3], np.nan) # Test for specific autocovariances acov1 = res.smoothed_state_autocovariance(1, t=0) assert_allclose(acov1, np.nan) acov1 = res.smoothed_state_autocovariance(1, t=1) assert_allclose(acov1[:2, :2], desired_acov1[1], rtol=1e-6, atol=1e-6) acov1 = res.smoothed_state_autocovariance( 1, start=8, end=9).transpose(2, 0, 1) assert_allclose(acov1[:, :2, :2], desired_acov1[8:9], rtol=1e-6, atol=1e-6) acov2 = res.smoothed_state_autocovariance(2, t=0) assert_allclose(acov2, np.nan) acov2 = res.smoothed_state_autocovariance(2, t=1) assert_allclose(acov2, np.nan) acov2 = res.smoothed_state_autocovariance(2, t=2) assert_allclose(acov2[:2, :2], desired_acov2[2], rtol=1e-6, atol=1e-6) acov2 = res.smoothed_state_autocovariance( 2, start=8, end=9).transpose(2, 0, 1) assert_allclose(acov2[:, :2, :2], desired_acov2[8:9], rtol=1e-6, atol=1e-6) @pytest.mark.parametrize('missing', ['all', 'partial', 'mixed', None]) @pytest.mark.parametrize('filter_univariate', [True, False]) @pytest.mark.parametrize('tvp', [True, False]) def test_smoothed_state_autocovariances_forwards(missing, filter_univariate, tvp): r""" Test for Cov(t, t + lag) """ # Out-of-sample model # Note: in TVP case, we need to first generate the larger model, and then # create the smaller model with the system matrices from the larger model # (otherwise they will be different, since the matrices are randomly # generated) mod_oos, res_oos = get_acov_model(missing, filter_univariate, tvp, oos=3) # Basic model names = ['obs_intercept', 'design', 'obs_cov', 'transition', 'selection', 'state_cov'] if not tvp: mod, res = get_acov_model(missing, filter_univariate, tvp, params=mod_oos.start_params) else: mod, _ = get_acov_model(missing, filter_univariate, tvp) for name in names: mod[name] = mod_oos[name, ..., :-3] res = mod.ssm.smooth() extend_kwargs1 = {} extend_kwargs2 = {} if tvp: keys = ['obs_intercept', 'design', 'obs_cov', 'transition', 'selection', 'state_cov'] for key in keys: extend_kwargs1[key] = mod_oos[key, ..., -3:-2] extend_kwargs2[key] = mod_oos[key, ..., -3:-1] assert_allclose(res_oos.llf, res.llf) cov = res.smoothed_state_cov.transpose(2, 0, 1) desired_acov1 = cov[:, 2:4, :2] desired_acov2 = cov[:, 4:6, :2] desired_acov3 = cov[:, 6:8, :2] oos_cov = np.concatenate( (res_oos.smoothed_state_cov, res_oos.predicted_state_cov[..., -1:]), axis=2).transpose(2, 0, 1) # Test all "forwards" autocovariances: Cov(t, t+lag) # For Cov(t, t+lag), the first out-of-sample forward covariance, # Cov(T, T+1), is already available, so we dno't need extend kwaargs acov1 = res.smoothed_state_autocovariance(-1).transpose(2, 0, 1) assert_allclose(acov1[:-1, :2, :2], desired_acov1[1:]) assert_allclose(acov1[-2:, :2, :2], oos_cov[-5:-3, 2:4, :2]) acov2 = res.smoothed_state_autocovariance( -2, extend_kwargs=extend_kwargs1).transpose(2, 0, 1) assert_allclose(acov2[:-2, :2, :2], desired_acov2[2:]) assert_allclose(acov2[-2:, :2, :2], oos_cov[-4:-2, 4:6, :2]) acov3 = res.smoothed_state_autocovariance( -3, extend_kwargs=extend_kwargs2).transpose(2, 0, 1) assert_allclose(acov3[:-3, :2, :2], desired_acov3[3:]) assert_allclose(acov3[-3:, :2, :2], oos_cov[-4:-1, 6:8, :2]) # Test for specific autocovariances acov1 = res.smoothed_state_autocovariance( -1, t=mod.nobs, extend_kwargs=extend_kwargs1) assert_allclose(acov1[:2, :2], oos_cov[-3, 2:4, :2]) acov1 = res.smoothed_state_autocovariance(-1, t=0) assert_allclose(acov1[:2, :2], desired_acov1[0 + 1]) acov1 = res.smoothed_state_autocovariance( -1, start=8, end=9).transpose(2, 0, 1) assert_allclose(acov1[:, :2, :2], desired_acov1[8 + 1:9 + 1]) acov2 = res.smoothed_state_autocovariance( -2, t=mod.nobs, extend_kwargs=extend_kwargs2) assert_allclose(acov2[:2, :2], oos_cov[-2, 4:6, :2]) acov2 = res.smoothed_state_autocovariance( -2, t=mod.nobs - 1, extend_kwargs=extend_kwargs1) assert_allclose(acov2[:2, :2], oos_cov[-3, 4:6, :2]) acov2 = res.smoothed_state_autocovariance(-2, t=0) assert_allclose(acov2[:2, :2], desired_acov2[0 + 2]) acov2 = res.smoothed_state_autocovariance( -2, start=8, end=9).transpose(2, 0, 1) assert_allclose(acov2[:, :2, :2], desired_acov2[8 + 2:9 + 2]) @pytest.mark.parametrize('missing', ['all', 'partial', 'mixed', None]) @pytest.mark.parametrize('filter_univariate', [True, False]) @pytest.mark.parametrize('tvp', [True, False]) def test_smoothed_state_autocovariances_forwards_oos(missing, filter_univariate, tvp): # Out-of-sample model # Note: in TVP case, we need to first generate the larger model, and then # create the smaller model with the system matrices from the larger model # (otherwise they will be different, since the matrices are randomly # generated) mod_oos, res_oos = get_acov_model(missing, filter_univariate, tvp, oos=5) # Basic model names = ['obs_intercept', 'design', 'obs_cov', 'transition', 'selection', 'state_cov'] if not tvp: mod, res = get_acov_model(missing, filter_univariate, tvp, params=mod_oos.start_params) else: mod, _ = get_acov_model(missing, filter_univariate, tvp) for name in names: mod[name] = mod_oos[name, ..., :-5] res = mod.ssm.smooth() assert_allclose(res_oos.llf, res.llf) cov = np.concatenate( (res_oos.smoothed_state_cov, res_oos.predicted_state_cov[..., -1:]), axis=2).transpose(2, 0, 1) desired_acov1 = cov[:, 2:4, :2] desired_acov2 = cov[:, 4:6, :2] desired_acov3 = cov[:, 6:8, :2] # Test all "forwards" autocovariances: Cov(t, t+lag) extend_kwargs = {} if tvp: extend_kwargs = { 'obs_intercept': mod_oos['obs_intercept', ..., -5:], 'design': mod_oos['design', ..., -5:], 'obs_cov': mod_oos['obs_cov', ..., -5:], 'transition': mod_oos['transition', ..., -5:], 'selection': mod_oos['selection', ..., -5:], 'state_cov': mod_oos['state_cov', ..., -5:]} # Note: we can compute up to Cov(mod_oos.nobs, mod_oos.nobs + 1) using # a model that has state space matrices defined up to mod_oos.nobs. Since # mod_oos.nobs = mod.nobs + 5, we need to pass in 5 additional time points, # and that is what extend_kwargs, above, does. acov1 = res.smoothed_state_autocovariance( -1, end=mod_oos.nobs, extend_kwargs=extend_kwargs).transpose(2, 0, 1) assert_equal(acov1.shape, (mod_oos.nobs, mod.k_states, mod.k_states)) assert_allclose(acov1[:, :2, :2], desired_acov1[1:]) # Note: now we can compute up to Cov(mod_oos.nobs - 1, mod_oos.nobs + 1) # using a model that has state space matrices defined up to mod_oos.nobs. # We still need to pass in 5 additional time points for the extend kwargs. # This is why we have end = mod_oos.nobs - 1, because this function returns # values through Cov(end, end + 2). Because start=0 (the default), we # will have values for Cov(0, 2), Cov(1, 3), ..., # Cov(mod_oos.nobs - 1, mod_oos.nobs + 1), and that is a set of # mod_oos.nobs - 1 matrices. acov2 = res.smoothed_state_autocovariance( -2, end=mod_oos.nobs - 1, extend_kwargs=extend_kwargs).transpose(2, 0, 1) assert_equal(acov2.shape, (mod_oos.nobs - 1, mod.k_states, mod.k_states)) assert_allclose(acov2[:, :2, :2], desired_acov2[2:]) # Note: now we can compute up to Cov(mod_oos.nobs - 2, mod_oos.nobs + 1) # using a model that has state space matrices defined up to mod_oos.nobs. # We still need to pass in 5 additional time points for the extend kwargs. acov3 = res.smoothed_state_autocovariance( -3, end=mod_oos.nobs - 2, extend_kwargs=extend_kwargs).transpose(2, 0, 1) assert_equal(acov3.shape, (mod_oos.nobs - 2, mod.k_states, mod.k_states)) assert_allclose(acov3[:, :2, :2], desired_acov3[3:]) @pytest.mark.parametrize('missing', ['all', 'partial', 'mixed', None]) @pytest.mark.parametrize('filter_univariate', [True, False]) @pytest.mark.parametrize('tvp', [True, False]) def test_smoothed_state_autocovariances_backwards_oos(missing, filter_univariate, tvp): # Out-of-sample model # Note: in TVP case, we need to first generate the larger model, and then # create the smaller model with the system matrices from the larger model # (otherwise they will be different, since the matrices are randomly # generated) mod_oos, res_oos = get_acov_model(missing, filter_univariate, tvp, oos=5) # Basic model names = ['obs_intercept', 'design', 'obs_cov', 'transition', 'selection', 'state_cov'] if not tvp: mod, res = get_acov_model(missing, filter_univariate, tvp, params=mod_oos.start_params) else: mod, _ = get_acov_model(missing, filter_univariate, tvp) for name in names: mod[name] = mod_oos[name, ..., :-5] res = mod.ssm.smooth() assert_allclose(res_oos.llf, res.llf) cov = np.concatenate( (res_oos.smoothed_state_cov, res_oos.predicted_state_cov[..., -1:]), axis=2).transpose(2, 0, 1) desired_acov1 = cov[:, :2, 2:4] desired_acov2 = cov[:, :2, 4:6] desired_acov3 = cov[:, :2, 6:8] # Test all "backwards" autocovariances: Cov(t, t - lag) end = mod_oos.nobs + 1 extend_kwargs = {} if tvp: extend_kwargs = { 'obs_intercept': mod_oos['obs_intercept', ..., -5:], 'design': mod_oos['design', ..., -5:], 'obs_cov': mod_oos['obs_cov', ..., -5:], 'transition': mod_oos['transition', ..., -5:], 'selection': mod_oos['selection', ..., -5:], 'state_cov': mod_oos['state_cov', ..., -5:]} # Note: we can compute up to Cov(mod_oos.nobs + 1, mod_oos.nobs) using # a model that has state space matrices defined up to mod_oos.nobs. Since # mod_oos.nobs = mod.nobs + 5, we need to pass in 5 additional time points, # and that is what extend_kwargs, above, does. acov1 = res.smoothed_state_autocovariance( 1, end=end, extend_kwargs=extend_kwargs).transpose(2, 0, 1) assert_equal(acov1.shape, (mod_oos.nobs + 1, mod.k_states, mod.k_states)) assert_allclose(acov1[1:, :2, :2], desired_acov1[1:]) # We cannot compute Cov(1, 0), so this is always NaNs assert_equal(acov1[:1], np.nan) # Note: we can compute up to Cov(mod_oos.nobs + 1, mod_oos.nobs - 1) using # a model that has state space matrices defined up to mod_oos.nobs, which # is why we don't need to change `end` here relative to the lag=1 case acov2 = res.smoothed_state_autocovariance( 2, end=end, extend_kwargs=extend_kwargs).transpose(2, 0, 1) assert_allclose(acov2[2:, :2, :2], desired_acov2[2:]) # We cannot compute Cov(1, -1) or Cov(2, 0), so this is always NaNs assert_equal(acov2[:2], np.nan) # Note: we can compute up to Cov(mod_oos.nobs + 1, mod_oos.nobs - 2) using # a model that has state space matrices defined up to mod_oos.nobs, which # is why we don't need to change `end` here relative to the lag=1 or lag=2 # cases acov3 = res.smoothed_state_autocovariance( 3, end=end, extend_kwargs=extend_kwargs).transpose(2, 0, 1) assert_allclose(acov3[3:, :2, :2], desired_acov3[3:]) # We cannot compute Cov(1, -2), Cov(2, -1), or Cov(3, 0), so this is always # NaNs assert_equal(acov3[:3], np.nan) def test_smoothed_state_autocovariances_invalid(): # Tests for invalid calls of `smoothed_state_autocovariance` _, res = get_acov_model(missing=False, filter_univariate=False, tvp=False) with pytest.raises(ValueError, match='Cannot specify both `t`'): res.smoothed_state_autocovariance(1, t=1, start=1) with pytest.raises(ValueError, match='Negative `t`'): res.smoothed_state_autocovariance(1, t=-1) with pytest.raises(ValueError, match='Negative `t`'): res.smoothed_state_autocovariance(1, start=-1) with pytest.raises(ValueError, match='Negative `t`'): res.smoothed_state_autocovariance(1, end=-1) with pytest.raises(ValueError, match='`end` must be after `start`'): res.smoothed_state_autocovariance(1, start=5, end=4) @pytest.mark.parametrize('missing', ['all', 'partial', 'mixed', None]) @pytest.mark.parametrize('filter_univariate', [True, False]) @pytest.mark.parametrize('tvp', [True, False]) def test_news_basic(missing, filter_univariate, tvp): # Basic tests for news # Get the basic model mod, res = get_acov_model(missing, filter_univariate, tvp) params = [] if tvp else mod.start_params # Get an expanded model with one new observation and 9 additional NaN # datapoints (so that we can compute the desired value using the # `smoothed_forecasts` attribute). append = np.zeros((10, 2)) * np.nan append[0] = [0.1, -0.2] endog2 = np.concatenate((mod.endog, append), axis=0) mod2 = mod.clone(endog2) res2 = mod2.smooth(params, return_ssm=True) # Get an expanded model with only 10 additional NaN datapoints, to compute # the baseline `smoothed_forecasts`. endog3 = endog2.copy() endog3[-10:] = np.nan mod3 = mod2.clone(endog3) res3 = mod3.smooth(params, return_ssm=True) # Test the news computation at the start, middle, and end of the sample, as # well as out-of-sample. for t in [0, 1, 150, mod.nobs - 1, mod.nobs, mod.nobs + 1, mod.nobs + 9]: # Test with a time argument out = res2.news(res, t=t) desired = (res2.smoothed_forecasts[..., t] - res3.smoothed_forecasts[..., t]) # The "news" about the t=0 smoothed forecast from new data at # observation t=202 is almost identically zero, so we need to set an # "atol" to avoid problems with comparing floating point versions of # zero. assert_allclose(out.update_impacts, desired, atol=1e-14) assert_equal(out.revision_impacts, None) # Test with start/end arguments out = res2.news(res, start=t, end=t + 1) assert_allclose(out.update_impacts, desired[None, ...], atol=1e-14) @pytest.mark.parametrize('missing', ['all', 'partial', 'mixed', None]) @pytest.mark.parametrize('filter_univariate', [True, False]) @pytest.mark.parametrize('tvp', [True, False]) def test_news_revisions(missing, filter_univariate, tvp): # Tests for news when there are revisions in the model # Get the basic model mod, res = get_acov_model(missing, filter_univariate, tvp, oos=10) params = [] if tvp else mod.start_params endog2 = mod.endog.copy() # Revise the last datapoint endog2[-11] = [0.0, 0.0] # Add a new datapoint endog2[-10] = [-0.3, -0.4] mod2 = mod.clone(endog2) res2 = mod2.smooth(params, return_ssm=True) # Test the news computation at the start, middle, and end of the sample, as # well as out-of-sample. nobs = mod.nobs - 10 for t in [0, 1, 150, nobs - 1, nobs, nobs + 1, nobs + 9]: out = res2.news(res, t=t) # Test for the news desired = (res2.smoothed_forecasts[..., t] - out.revision_results.smoothed_forecasts[..., t]) # Relaxed tolerance to 1e-10 after random failures assert_allclose(out.update_impacts, desired, atol=1e-10) # Test for the revisions desired = (out.revision_results.smoothed_forecasts[..., t] - res.smoothed_forecasts[..., t]) # Relaxed tolerance to 1e-10 after random failures assert_allclose(out.revision_impacts, desired, atol=1e-10) @pytest.mark.parametrize('missing', ['all', 'partial', 'mixed', None]) @pytest.mark.parametrize('filter_univariate', [True, False]) @pytest.mark.parametrize('tvp', [True, False]) def test_news_invalid(missing, filter_univariate, tvp): # Tests for invalid calls to news # (generic error message used below) error_ss = ('This results object has %s and so it does not appear to' ' by an extension of `previous`. Can only compute the' ' news by comparing this results set to previous results' ' objects.') # Basic model / results setup mod, res = get_acov_model(missing, filter_univariate, tvp, oos=1) params = [] if tvp else mod.start_params endog2 = mod.endog.copy() endog2[-1] = [0.2, 0.5] mod2 = mod.clone(endog2) res2_filtered = mod2.filter(params, return_ssm=True) res2_smoothed = mod2.smooth(params, return_ssm=True) # Test that news works with smoothing, but not with only filtering res2_smoothed.news(res, t=mod.nobs - 1) msg = ('Cannot compute news without having' ' applied the Kalman smoother first.') with pytest.raises(ValueError, match=msg): res2_filtered.news(res, t=mod.nobs - 1) # Test that if we want to request news for an out-of-sample period in a # time-varying model, then we need to provide a new design matrix if tvp: msg = ('Cannot compute the impacts of news on periods outside of the' ' sample in time-varying models.') with pytest.raises(RuntimeError, match=msg): res2_smoothed.news(res, t=mod.nobs + 2) # Test that news won't work when the calling model is is smaller mod, res = get_acov_model(missing, filter_univariate, tvp) params = [] if tvp else mod.start_params endog2 = mod.endog.copy()[:mod.nobs - 1] mod2 = mod.clone(endog2) res2 = mod2.smooth(params, return_ssm=True) msg = error_ss % 'fewer observations than `previous`' with pytest.raises(ValueError, match=msg): res2.news(res, t=mod.nobs - 1) # Test that news won't work when the state dimensions are different mod2 = sarimax.SARIMAX(np.zeros(mod.nobs)) res2 = mod2.smooth([0.5, 1.], return_ssm=True) msg = error_ss % 'different state space dimensions than `previous`' with pytest.raises(ValueError, match=msg): res2.news(res, t=mod.nobs - 1) # Test that news won't work when one of the models is time-varying and one # is time-invariant mod2, res2 = get_acov_model(missing, filter_univariate, not tvp, oos=1) if tvp: msg = 'time-invariant design while `previous` does not' else: msg = 'time-varying design while `previous` does not' with pytest.raises(ValueError, match=msg): res2.news(res, t=mod.nobs - 1)