155 lines
6.3 KiB
Matlab
155 lines
6.3 KiB
Matlab
function [LIK,lik] = auxiliary_particle_filter(ReducedForm,Y,start,ParticleOptions,ThreadsOptions)
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% Evaluates the likelihood of a nonlinear model with the auxiliary particle filter
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% allowing eventually resampling.
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%
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% Copyright (C) 2011-2015 Dynare Team
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%
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% This file is part of Dynare (particles module).
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare particles module is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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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 number_of_particles
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persistent sample_size number_of_observed_variables number_of_structural_innovations
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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 flag for prunning
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pruning = ParticleOptions.pruning;
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% Get steady state and mean.
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steadystate = ReducedForm.steadystate;
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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_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_observed_variables = length(mf1);
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number_of_structural_innovations = length(ReducedForm.Q);
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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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% 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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% Get covariance matrices
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Q = ReducedForm.Q;
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H = ReducedForm.H;
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% Get initial condition for the state vector.
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StateVectorMean = ReducedForm.StateVectorMean;
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StateVectorVarianceSquareRoot = chol(ReducedForm.StateVectorVariance)';
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state_variance_rank = size(StateVectorVarianceSquareRoot,2);
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Q_lower_triangular_cholesky = chol(Q)';
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% Set seed for randn().
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set_dynare_seed('default');
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% Initialization of the likelihood.
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const_lik = log(2*pi)*number_of_observed_variables+log(det(H));
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lik = NaN(sample_size,1);
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LIK = NaN;
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% Initialization of the weights across particles.
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weights = ones(1,number_of_particles)/number_of_particles ;
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StateVectors = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean);
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%StateVectors = bsxfun(@plus,zeros(state_variance_rank,number_of_particles),StateVectorMean);
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if pruning
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StateVectors_ = StateVectors;
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end
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% Uncomment for building the mean average predictions based on a sparse
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% grids of structural shocks. Otherwise, all shocks are set to 0 in the
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% prediction.
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%if ParticleOptions.proposal_approximation.cubature
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% [nodes,nodes_weights] = spherical_radial_sigma_points(number_of_structural_innovations) ;
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% nodes_weights = ones(size(nodes,1),1)*nodes_weights ;
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%elseif ParticleOptions.proposal_approximation.unscented
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% [nodes,nodes_weights,nodes_weights_c] = unscented_sigma_points(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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%end
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%nodes = Q_lower_triangular_cholesky*nodes ;
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nodes = zeros(1,number_of_structural_innovations) ;
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nodes_weights = 1 ;
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for t=1:sample_size
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yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
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if pruning
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yhat_ = bsxfun(@minus,StateVectors_,state_variables_steady_state);
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tmp = 0 ;
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tmp_ = 0 ;
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for i=1:size(nodes)
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[tmp1, tmp1_] = local_state_space_iteration_2(yhat,nodes(i,:)*ones(1,number_of_particles),ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,ThreadsOptions.local_state_space_iteration_2);
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tmp = tmp + nodes_weights(i)*tmp1 ;
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tmp_ = tmp_ + nodes_weights(i)*tmp1_ ;
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end
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else
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tmp = 0 ;
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for i=1:size(nodes)
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tmp = tmp + nodes_weights(i)*local_state_space_iteration_2(yhat,nodes(i,:)*ones(1,number_of_particles),ghx,ghu,constant,ghxx,ghuu,ghxu,ThreadsOptions.local_state_space_iteration_2);
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end
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end
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PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:));
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%tau_tilde = weights.*(exp(-.5*(const_lik+sum(PredictionError.*(H\PredictionError),1))) + 1e-99) ;
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% Replace Gaussian density with a Student density with 3 degrees of
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% freedom for fat tails.
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z = sum(PredictionError.*(H\PredictionError),1) ;
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tau_tilde = weights.*(tpdf(z,3*ones(size(z)))+1e-99) ;
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tau_tilde = tau_tilde/sum(tau_tilde) ;
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indx = resample(0,tau_tilde',ParticleOptions);
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if pruning
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yhat_ = yhat_(:,indx) ;
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end
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yhat = yhat(:,indx) ;
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weights_stage_1 = weights(indx)./tau_tilde(indx) ;
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epsilon = Q_lower_triangular_cholesky*randn(number_of_structural_innovations,number_of_particles);
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if pruning
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[tmp, tmp_] = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,ThreadsOptions.local_state_space_iteration_2);
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StateVectors_ = tmp_(mf0,:);
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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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StateVectors = tmp(mf0,:);
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PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:));
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weights_stage_2 = weights_stage_1.*(exp(-.5*(const_lik+sum(PredictionError.*(H\PredictionError),1))) + 1e-99) ;
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lik(t) = log(mean(weights_stage_2)) ;
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weights = weights_stage_2/sum(weights_stage_2);
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if (ParticleOptions.resampling.status.generic && neff(weights)<ParticleOptions.resampling.threshold*sample_size) || ParticleOptions.resampling.status.systematic
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if pruning
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temp = resample([StateVectors' StateVectors_'],weights',ParticleOptions);
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StateVectors = temp(:,1:number_of_state_variables)';
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StateVectors_ = temp(:,number_of_state_variables+1:2*number_of_state_variables)';
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else
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StateVectors = resample(StateVectors',weights',ParticleOptions)';
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end
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weights = ones(1,number_of_particles)/number_of_particles;
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end
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end
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%plot(lik) ;
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LIK = -sum(lik(start:end)); |