parent
89a941605f
commit
472d755d98
GPG Key ID:
295C1FE89E17EB3C
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@ -1,4 +1,4 @@
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function IncrementalWeights = gaussian_densities(obs,mut_t,sqr_Pss_t_t,st_t_1,sqr_Pss_t_t_1,particles,H,normconst,weigths1,weigths2,ReducedForm,ThreadsOptions)
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function IncrementalWeights = gaussian_densities(obs,mut_t,sqr_Pss_t_t,st_t_1,sqr_Pss_t_t_1,particles,H,normconst,weigths1,weigths2,ReducedForm,ThreadsOptions,DynareOptions, Model)
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%
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% Elements to calculate the importance sampling ratio
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%
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@ -19,7 +19,8 @@ function IncrementalWeights = gaussian_densities(obs,mut_t,sqr_Pss_t_t,st_t_1,sq
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%
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% NOTES
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% The vector "lik" is used to evaluate the jacobian of the likelihood.
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% Copyright (C) 2009-2017 Dynare Team
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% Copyright (C) 2009-2019 Dynare Team
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%
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% This file is part of Dynare.
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%
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@ -37,17 +38,13 @@ function IncrementalWeights = gaussian_densities(obs,mut_t,sqr_Pss_t_t,st_t_1,sq
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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% proposal density
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proposal = probability2(mut_t,sqr_Pss_t_t,particles) ;
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proposal = probability2(mut_t, sqr_Pss_t_t, particles);
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% prior density
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prior = probability2(st_t_1,sqr_Pss_t_t_1,particles) ;
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prior = probability2(st_t_1, sqr_Pss_t_t_1, particles);
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% likelihood
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yt_t_1_i = measurement_equations(particles,ReducedForm,ThreadsOptions) ;
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%eta_t_i = bsxfun(@minus,obs,yt_t_1_i)' ;
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%yt_t_1 = sum(yt_t_1_i*weigths1,2) ;
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%tmp = bsxfun(@minus,yt_t_1_i,yt_t_1) ;
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%Pyy = bsxfun(@times,weigths2',tmp)*tmp' + H ;
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%sqr_det = sqrt(det(Pyy)) ;
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%foo = (eta_t_i/Pyy).*eta_t_i ;
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%likelihood = exp(-0.5*sum(foo,2))/(normconst*sqr_det) + 1e-99 ;
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likelihood = probability2(obs,sqrt(H),yt_t_1_i) ;
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IncrementalWeights = likelihood.*prior./proposal ;
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yt_t_1_i = measurement_equations(particles, ReducedForm, ThreadsOptions, DynareOptions, Model);
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likelihood = probability2(obs, sqrt(H), yt_t_1_i);
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IncrementalWeights = likelihood.*prior./proposal;
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@ -1,4 +1,5 @@
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function [LIK,lik] = gaussian_filter(ReducedForm, Y, start, ParticleOptions, ThreadsOptions)
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function [LIK,lik] = gaussian_filter(ReducedForm, Y, start, ParticleOptions, ThreadsOptions, DynareOptions, Model)
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% Evaluates the likelihood of a non-linear model approximating the
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% predictive (prior) and filtered (posterior) densities for state variables
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% by gaussian distributions.
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@ -30,7 +31,8 @@ function [LIK,lik] = gaussian_filter(ReducedForm, Y, start, ParticleOptions, Thr
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%
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% NOTES
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% The vector "lik" is used to evaluate the jacobian of the likelihood.
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% Copyright (C) 2009-2017 Dynare Team
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% Copyright (C) 2009-2019 Dynare Team
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%
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% This file is part of Dynare.
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%
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@ -47,37 +49,27 @@ function [LIK,lik] = gaussian_filter(ReducedForm, Y, start, ParticleOptions, Thr
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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persistent init_flag mf0 mf1
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persistent nodes2 weights2 weights_c2 number_of_particles
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persistent sample_size number_of_state_variables number_of_observed_variables
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% Set default
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if isempty(start)
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start = 1;
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end
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% Set persistent variables.
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if isempty(init_flag)
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mf0 = ReducedForm.mf0;
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mf1 = ReducedForm.mf1;
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sample_size = size(Y,2);
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number_of_state_variables = length(mf0);
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number_of_observed_variables = length(mf1);
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number_of_particles = ParticleOptions.number_of_particles;
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init_flag = 1;
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end
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mf0 = ReducedForm.mf0;
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mf1 = ReducedForm.mf1;
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sample_size = size(Y,2);
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number_of_state_variables = length(mf0);
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number_of_observed_variables = length(mf1);
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number_of_particles = ParticleOptions.number_of_particles;
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% compute gaussian quadrature nodes and weights on states and shocks
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if isempty(nodes2)
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if ParticleOptions.distribution_approximation.cubature
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[nodes2,weights2] = spherical_radial_sigma_points(number_of_state_variables);
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weights_c2 = weights2;
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elseif ParticleOptions.distribution_approximation.unscented
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[nodes2,weights2,weights_c2] = unscented_sigma_points(number_of_state_variables,ParticleOptions);
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else
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if ~ParticleOptions.distribution_approximation.montecarlo
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error('Estimation: This approximation for the proposal is not implemented or unknown!')
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end
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if ParticleOptions.distribution_approximation.cubature
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[nodes2, weights2] = spherical_radial_sigma_points(number_of_state_variables);
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weights_c2 = weights2;
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elseif ParticleOptions.distribution_approximation.unscented
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[nodes2, weights2, weights_c2] = unscented_sigma_points(number_of_state_variables,ParticleOptions);
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else
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if ~ParticleOptions.distribution_approximation.montecarlo
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error('This approximation for the proposal is unknown!')
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end
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end
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@ -107,38 +99,37 @@ lik = NaN(sample_size,1);
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LIK = NaN;
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for t=1:sample_size
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[PredictedStateMean,PredictedStateVarianceSquareRoot,StateVectorMean,StateVectorVarianceSquareRoot] = ...
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gaussian_filter_bank(ReducedForm,Y(:,t),StateVectorMean,StateVectorVarianceSquareRoot,Q_lower_triangular_cholesky,H_lower_triangular_cholesky,H,ParticleOptions,ThreadsOptions) ;
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[PredictedStateMean, PredictedStateVarianceSquareRoot, StateVectorMean, StateVectorVarianceSquareRoot] = ...
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gaussian_filter_bank(ReducedForm, Y(:,t), StateVectorMean, StateVectorVarianceSquareRoot, Q_lower_triangular_cholesky, H_lower_triangular_cholesky, ...
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H, ParticleOptions, ThreadsOptions, DynareOptions, Model);
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if ParticleOptions.distribution_approximation.cubature || ParticleOptions.distribution_approximation.unscented
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StateParticles = bsxfun(@plus,StateVectorMean,StateVectorVarianceSquareRoot*nodes2') ;
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IncrementalWeights = ...
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gaussian_densities(Y(:,t),StateVectorMean,...
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StateVectorVarianceSquareRoot,PredictedStateMean,...
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PredictedStateVarianceSquareRoot,StateParticles,H,const_lik,...
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weights2,weights_c2,ReducedForm,ThreadsOptions) ;
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SampleWeights = weights2.*IncrementalWeights ;
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StateParticles = bsxfun(@plus, StateVectorMean, StateVectorVarianceSquareRoot*nodes2');
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IncrementalWeights = gaussian_densities(Y(:,t), StateVectorMean, StateVectorVarianceSquareRoot, PredictedStateMean, ...
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PredictedStateVarianceSquareRoot, StateParticles, H, const_lik, ...
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weights2, weights_c2, ReducedForm, ThreadsOptions, ...
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DynareOptions, Model);
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SampleWeights = weights2.*IncrementalWeights;
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else
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StateParticles = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean) ;
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IncrementalWeights = ...
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gaussian_densities(Y(:,t),StateVectorMean,...
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StateVectorVarianceSquareRoot,PredictedStateMean,...
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PredictedStateVarianceSquareRoot,StateParticles,H,const_lik,...
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1/number_of_particles,1/number_of_particles,ReducedForm,ThreadsOptions) ;
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SampleWeights = IncrementalWeights/number_of_particles ;
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StateParticles = bsxfun(@plus, StateVectorVarianceSquareRoot*randn(state_variance_rank, number_of_particles), StateVectorMean) ;
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IncrementalWeights = gaussian_densities(Y(:,t), StateVectorMean, StateVectorVarianceSquareRoot, PredictedStateMean, ...
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PredictedStateVarianceSquareRoot,StateParticles,H,const_lik, ...
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1/number_of_particles,1/number_of_particles,ReducedForm,ThreadsOptions, ...
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DynareOptions, Model);
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SampleWeights = IncrementalWeights/number_of_particles;
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end
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SampleWeights = SampleWeights + 1e-6*ones(size(SampleWeights,1),1) ;
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SumSampleWeights = sum(SampleWeights) ;
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lik(t) = log(SumSampleWeights) ;
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SampleWeights = SampleWeights./SumSampleWeights ;
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SampleWeights = SampleWeights + 1e-6*ones(size(SampleWeights, 1), 1);
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SumSampleWeights = sum(SampleWeights);
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lik(t) = log(SumSampleWeights);
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SampleWeights = SampleWeights./SumSampleWeights;
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if not(ParticleOptions.distribution_approximation.cubature || ParticleOptions.distribution_approximation.unscented)
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if (ParticleOptions.resampling.status.generic && neff(SampleWeights)<ParticleOptions.resampling.threshold*sample_size) || ParticleOptions.resampling.status.systematic
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StateParticles = resample(StateParticles',SampleWeights,ParticleOptions)' ;
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SampleWeights = ones(number_of_particles,1)/number_of_particles;
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StateParticles = resample(StateParticles', SampleWeights, ParticleOptions)';
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SampleWeights = ones(number_of_particles, 1)/number_of_particles;
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end
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end
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StateVectorMean = StateParticles*SampleWeights ;
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temp = bsxfun(@minus,StateParticles,StateVectorMean) ;
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StateVectorVarianceSquareRoot = reduced_rank_cholesky( bsxfun(@times,SampleWeights',temp)*temp' )';
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StateVectorMean = StateParticles*SampleWeights;
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temp = bsxfun(@minus, StateParticles, StateVectorMean);
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StateVectorVarianceSquareRoot = reduced_rank_cholesky(bsxfun(@times,SampleWeights',temp)*temp')';
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end
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LIK = -sum(lik(start:end));
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LIK = -sum(lik(start:end));
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function [PredictedStateMean,PredictedStateVarianceSquareRoot,StateVectorMean,StateVectorVarianceSquareRoot] = gaussian_filter_bank(ReducedForm,obs,StateVectorMean,StateVectorVarianceSquareRoot,Q_lower_triangular_cholesky,H_lower_triangular_cholesky,H,ParticleOptions,ThreadsOptions)
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function [PredictedStateMean, PredictedStateVarianceSquareRoot, StateVectorMean, StateVectorVarianceSquareRoot] = ...
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gaussian_filter_bank(ReducedForm, obs, StateVectorMean, StateVectorVarianceSquareRoot, Q_lower_triangular_cholesky, H_lower_triangular_cholesky, H, ...
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ParticleOptions, ThreadsOptions, DynareOptions, Model)
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%
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% Computes the proposal with a gaussian approximation for importance
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% sampling
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@ -19,6 +21,7 @@ function [PredictedStateMean,PredictedStateVarianceSquareRoot,StateVectorMean,St
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%
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% NOTES
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% The vector "lik" is used to evaluate the jacobian of the likelihood.
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% Copyright (C) 2009-2017 Dynare Team
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%
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% This file is part of Dynare.
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@ -36,83 +39,73 @@ function [PredictedStateMean,PredictedStateVarianceSquareRoot,StateVectorMean,St
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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persistent init_flag2 mf0 mf1
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persistent number_of_state_variables number_of_observed_variables
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persistent number_of_structural_innovations
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% Set local state space model (first-order approximation).
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ghx = ReducedForm.ghx;
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ghu = ReducedForm.ghu;
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% Set local state space model (second-order approximation).
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ghxx = ReducedForm.ghxx;
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ghuu = ReducedForm.ghuu;
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ghxu = ReducedForm.ghxu;
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if any(any(isnan(ghx))) || any(any(isnan(ghu))) || any(any(isnan(ghxx))) || any(any(isnan(ghuu))) || any(any(isnan(ghxu))) || ...
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any(any(isinf(ghx))) || any(any(isinf(ghu))) || any(any(isinf(ghxx))) || any(any(isinf(ghuu))) || any(any(isinf(ghxu))) ...
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any(any(abs(ghx)>1e4)) || any(any(abs(ghu)>1e4)) || any(any(abs(ghxx)>1e4)) || any(any(abs(ghuu)>1e4)) || any(any(abs(ghxu)>1e4))
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ghx
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ghu
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ghxx
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ghuu
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ghxu
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if ReducedForm.use_k_order_solver
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dr = ReducedForm.dr;
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else
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% Set local state space model (first-order approximation).
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ghx = ReducedForm.ghx;
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ghu = ReducedForm.ghu;
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% Set local state space model (second-order approximation).
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ghxx = ReducedForm.ghxx;
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ghuu = ReducedForm.ghuu;
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ghxu = ReducedForm.ghxu;
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end
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constant = ReducedForm.constant;
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state_variables_steady_state = ReducedForm.state_variables_steady_state;
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% Set persistent variables.
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if isempty(init_flag2)
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mf0 = ReducedForm.mf0;
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mf1 = ReducedForm.mf1;
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number_of_state_variables = length(mf0);
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number_of_observed_variables = length(mf1);
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number_of_structural_innovations = length(ReducedForm.Q);
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init_flag2 = 1;
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end
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mf0 = ReducedForm.mf0;
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mf1 = ReducedForm.mf1;
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number_of_state_variables = length(mf0);
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number_of_observed_variables = length(mf1);
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number_of_structural_innovations = length(ReducedForm.Q);
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if ParticleOptions.proposal_approximation.montecarlo
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nodes = randn(ParticleOptions.number_of_particles,number_of_state_variables+number_of_structural_innovations) ;
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nodes = randn(ParticleOptions.number_of_particles, number_of_state_variables+number_of_structural_innovations) ;
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weights = 1/ParticleOptions.number_of_particles ;
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weights_c = weights ;
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elseif ParticleOptions.proposal_approximation.cubature
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[nodes,weights] = spherical_radial_sigma_points(number_of_state_variables+number_of_structural_innovations) ;
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weights_c = weights ;
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elseif ParticleOptions.proposal_approximation.unscented
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[nodes,weights,weights_c] = unscented_sigma_points(number_of_state_variables+number_of_structural_innovations,ParticleOptions);
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[nodes,weights,weights_c] = unscented_sigma_points(number_of_state_variables+number_of_structural_innovations, ParticleOptions);
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else
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error('Estimation: This approximation for the proposal is not implemented or unknown!')
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error('This approximation for the proposal is not implemented or unknown!')
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end
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xbar = [StateVectorMean ; zeros(number_of_structural_innovations,1) ] ;
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sqr_Px = [ [ StateVectorVarianceSquareRoot zeros(number_of_state_variables,number_of_structural_innovations) ] ;
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[ zeros(number_of_structural_innovations,number_of_state_variables) Q_lower_triangular_cholesky ] ];
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sigma_points = bsxfun(@plus,xbar,sqr_Px*(nodes'));
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xbar = [StateVectorMean ; zeros(number_of_structural_innovations,1)] ;
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sqr_Px = [ StateVectorVarianceSquareRoot, zeros(number_of_state_variables, number_of_structural_innovations);
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zeros(number_of_structural_innovations, number_of_state_variables) Q_lower_triangular_cholesky];
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sigma_points = bsxfun(@plus, xbar, sqr_Px*(nodes'));
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StateVectors = sigma_points(1:number_of_state_variables,:);
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epsilon = sigma_points(number_of_state_variables+1:number_of_state_variables+number_of_structural_innovations,:);
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yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
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tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,ThreadsOptions.local_state_space_iteration_2);
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PredictedStateMean = tmp(mf0,:)*weights ;
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yhat = bsxfun(@minus, StateVectors, state_variables_steady_state);
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if ReducedForm.use_k_order_solver
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tmp = local_state_space_iteration_k(yhat, epsilon, dr, Model, DynareOptions);
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else
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tmp = local_state_space_iteration_2(yhat, epsilon, ghx, ghu, constant, ghxx, ghuu, ghxu, ThreadsOptions.local_state_space_iteration_2);
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end
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PredictedStateMean = tmp(mf0,:)*weights;
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PredictedObservedMean = tmp(mf1,:)*weights;
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if ParticleOptions.proposal_approximation.cubature || ParticleOptions.proposal_approximation.montecarlo
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PredictedStateMean = sum(PredictedStateMean,2);
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PredictedObservedMean = sum(PredictedObservedMean,2);
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dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean)'.*sqrt(weights);
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dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean)'.*sqrt(weights);
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PredictedStateMean = sum(PredictedStateMean, 2);
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PredictedObservedMean = sum(PredictedObservedMean, 2);
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dState = bsxfun(@minus,tmp(mf0,:), PredictedStateMean)'.*sqrt(weights);
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dObserved = bsxfun(@minus, tmp(mf1,:), PredictedObservedMean)'.*sqrt(weights);
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PredictedStateVarianceSquareRoot = chol(dState'*dState)';
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big_mat = [dObserved dState ; [H_lower_triangular_cholesky zeros(number_of_observed_variables,number_of_state_variables)] ];
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[mat1,mat] = qr2(big_mat,0);
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big_mat = [dObserved, dState ; H_lower_triangular_cholesky, zeros(number_of_observed_variables,number_of_state_variables)];
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[~, mat] = qr2(big_mat, 0);
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mat = mat';
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clear('mat1');
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PredictedObservedVarianceSquareRoot = mat(1:number_of_observed_variables,1:number_of_observed_variables);
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CovarianceObservedStateSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),1:number_of_observed_variables);
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StateVectorVarianceSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),number_of_observed_variables+(1:number_of_state_variables));
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PredictionError = obs - PredictedObservedMean;
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StateVectorMean = PredictedStateMean + (CovarianceObservedStateSquareRoot/PredictedObservedVarianceSquareRoot)*PredictionError;
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else
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dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean);
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dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean);
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dState = bsxfun(@minus, tmp(mf0,:), PredictedStateMean);
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dObserved = bsxfun(@minus, tmp(mf1,:), PredictedObservedMean);
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PredictedStateVariance = dState*diag(weights_c)*dState';
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PredictedObservedVariance = dObserved*diag(weights_c)*dObserved' + H;
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PredictedStateAndObservedCovariance = dState*diag(weights_c)*dObserved';
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@ -123,4 +116,4 @@ else
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StateVectorVariance = PredictedStateVariance - KalmanFilterGain*PredictedObservedVariance*KalmanFilterGain';
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StateVectorVariance = .5*(StateVectorVariance+StateVectorVariance');
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StateVectorVarianceSquareRoot = reduced_rank_cholesky(StateVectorVariance)';
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end
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end
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@ -1,6 +1,6 @@
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function measure = measurement_equations(StateVectors,ReducedForm,ThreadsOptions)
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function measure = measurement_equations(StateVectors,ReducedForm,ThreadsOptions, DynareOptions, Model)
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% Copyright (C) 2013-2017 Dynare Team
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% Copyright (C) 2013-2019 Dynare Team
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%
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% This file is part of Dynare.
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%
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|
@ -18,13 +18,22 @@ function measure = measurement_equations(StateVectors,ReducedForm,ThreadsOptions
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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mf1 = ReducedForm.mf1;
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ghx = ReducedForm.ghx(mf1,:);
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ghu = ReducedForm.ghu(mf1,:);
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ghxx = ReducedForm.ghxx(mf1,:);
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ghuu = ReducedForm.ghuu(mf1,:);
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ghxu = ReducedForm.ghxu(mf1,:);
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if ReducedForm.use_k_order_solver
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dr = ReducedForm.dr;
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else
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ghx = ReducedForm.ghx(mf1,:);
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ghu = ReducedForm.ghu(mf1,:);
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ghxx = ReducedForm.ghxx(mf1,:);
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ghuu = ReducedForm.ghuu(mf1,:);
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ghxu = ReducedForm.ghxu(mf1,:);
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end
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constant = ReducedForm.constant(mf1,:);
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state_variables_steady_state = ReducedForm.state_variables_steady_state;
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number_of_structural_innovations = length(ReducedForm.Q);
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yhat = bsxfun(@minus,StateVectors,state_variables_steady_state) ;
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measure = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,size(yhat,2)),ghx,ghu,constant,ghxx,ghuu,ghxu,ThreadsOptions.local_state_space_iteration_2);
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yhat = bsxfun(@minus, StateVectors, state_variables_steady_state);
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if ReducedForm.use_k_order_solver
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tmp = local_state_space_iteration_k(yhat, zeros(number_of_structural_innovations, size(yhat,2)), dr, Model, DynareOptions);
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measure = tmp(mf1,:);
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else
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measure = local_state_space_iteration_2(yhat, zeros(number_of_structural_innovations, size(yhat,2)), ghx, ghu, constant, ghxx, ghuu, ghxu, ThreadsOptions.local_state_space_iteration_2);
|
||||
end
|
||||
Loading…
Reference in New Issue