165 lines
7.3 KiB
Matlab
165 lines
7.3 KiB
Matlab
function [ProposalStateVector, Weights, flag] = conditional_filter_proposal(ReducedForm, y, StateVectors, SampleWeights, Q_lower_triangular_cholesky, H_lower_triangular_cholesky, ...
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H, ParticleOptions, ThreadsOptions, options_, M_)
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% Computes the proposal for each past particle using Gaussian approximations
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% for the state errors and the Kalman filter
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%
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% INPUTS
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% - ReducedForm [structure] Matlab's structure describing the reduced form model.
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% - y [double] p×1 vector, current observation (p is the number of observed variables).
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% - StateVectors
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% - SampleWeights
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% - Q_lower_triangular_cholesky
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% - H_lower_triangular_cholesky
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% - H
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% - ParticleOptions
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% - ThreadsOptions
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% - options_
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% - M_
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%
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% OUTPUTS
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% - ProposalStateVector
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% - Weights
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% - flag
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% Copyright © 2012-2022 Dynare Team
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%
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% This file is part of Dynare.
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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 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 <https://www.gnu.org/licenses/>.
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flag = false;
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order = options_.order;
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if ReducedForm.use_k_order_solver
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dr = ReducedForm.dr;
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udr = ReducedForm.udr;
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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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ghs2 = ReducedForm.ghs2;
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if order == 3
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% Set local state space model (third order approximation).
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ghxxx = ReducedForm.ghxxx;
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ghuuu = ReducedForm.ghuuu;
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ghxxu = ReducedForm.ghxxu;
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ghxuu = ReducedForm.ghxuu;
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ghxss = ReducedForm.ghxss;
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ghuss = ReducedForm.ghuss;
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end
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end
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constant = ReducedForm.constant;
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steadystate = ReducedForm.steadystate;
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state_variables_steady_state = ReducedForm.state_variables_steady_state;
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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/10, number_of_structural_innovations);
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weights = 1.0/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_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_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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epsilon = Q_lower_triangular_cholesky*nodes';
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yhat = repmat(StateVectors-state_variables_steady_state, 1, size(epsilon, 2));
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if ReducedForm.use_k_order_solver
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tmp = local_state_space_iteration_k(yhat, epsilon, dr, M_, options_, udr);
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else
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if order == 2
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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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elseif order == 3
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tmp = local_state_space_iteration_3(yhat, epsilon, ghx, ghu, ghxx, ghuu, ghxu, ghs2, ghxxx, ghuuu, ghxxu, ghxuu, ghxss, ghuss, steadystate, ThreadsOptions.local_state_space_iteration_3, false);
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else
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error('Order > 3: use_k_order_solver should be set to true');
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end
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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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PredictedStateVariance = 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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[~, mat] = qr2(big_mat,0);
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mat = mat';
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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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Error = y-PredictedObservedMean;
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StateVectorMean = PredictedStateMean+(CovarianceObservedStateSquareRoot/PredictedObservedVarianceSquareRoot)*Error;
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if ParticleOptions.cpf_weights_method.amisanotristani
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Weights = SampleWeights.*probability2(zeros(number_of_observed_variables,1), PredictedObservedVarianceSquareRoot, Error);
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end
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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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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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KalmanFilterGain = PredictedStateAndObservedCovariance/PredictedObservedVariance;
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Error = y-PredictedObservedMean;
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StateVectorMean = PredictedStateMean+KalmanFilterGain*Error;
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StateVectorVariance = PredictedStateVariance-KalmanFilterGain*PredictedObservedVariance*KalmanFilterGain';
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StateVectorVariance = 0.5*(StateVectorVariance+StateVectorVariance');
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[StateVectorVarianceSquareRoot, p] = chol(StateVectorVariance, 'lower') ;
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if p
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flag = true;
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ProposalStateVector = zeros(number_of_state_variables, 1);
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Weights = 0.0;
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return
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end
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if ParticleOptions.cpf_weights_method.amisanotristani
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Weights = SampleWeights.*probability2(zeros(number_of_observed_variables, 1), chol(PredictedObservedVariance)', Error);
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end
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end
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ProposalStateVector = StateVectorVarianceSquareRoot*randn(size(StateVectorVarianceSquareRoot, 2), 1)+StateVectorMean;
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if ParticleOptions.cpf_weights_method.murrayjonesparslow
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PredictedStateVariance = 0.5*(PredictedStateVariance+PredictedStateVariance');
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[PredictedStateVarianceSquareRoot, p] = chol(PredictedStateVariance, 'lower');
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if p
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flag = true;
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ProposalStateVector = zeros(number_of_state_variables,1);
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Weights = 0.0;
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return
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end
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Prior = probability2(PredictedStateMean, PredictedStateVarianceSquareRoot, ProposalStateVector);
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Posterior = probability2(StateVectorMean, StateVectorVarianceSquareRoot, ProposalStateVector);
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Likelihood = probability2(y, H_lower_triangular_cholesky, measurement_equations(ProposalStateVector, ReducedForm, ThreadsOptions, options_, M_));
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Weights = SampleWeights.*Likelihood.*(Prior./Posterior);
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end
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