Allow k order approximation in conditional particle filter (cpf).
Ref. dynare#1673rm-particles^2
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313003b145
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2ed534e52e
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@ -1,24 +1,28 @@
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function [ProposalStateVector,Weights,flag] = conditional_filter_proposal(ReducedForm,obs,StateVectors,SampleWeights,Q_lower_triangular_cholesky,H_lower_triangular_cholesky,H,ParticleOptions,ThreadsOptions,normconst2)
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%
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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, DynareOptions, Model)
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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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% reduced_form_model [structure] Matlab's structure describing the reduced form model.
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% reduced_form_model.measurement.H [double] (pp x pp) variance matrix of measurement errors.
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% reduced_form_model.state.Q [double] (qq x qq) variance matrix of state errors.
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% reduced_form_model.state.dr [structure] output of resol.m.
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% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
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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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% - DynareOptions
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% - Model
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%
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% OUTPUTS
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% LIK [double] scalar, likelihood
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% lik [double] vector, density of observations in each period.
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%
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% REFERENCES
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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) 2012-2017 Dynare Team
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% - ProposalStateVector
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% - Weights
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% - flag
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% Copyright © 2012-2020 Dynare Team
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%
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% This file is part of Dynare.
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%
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@ -34,124 +38,107 @@ function [ProposalStateVector,Weights,flag] = conditional_filter_proposal(Reduce
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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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%
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% AUTHOR(S) frederic DOT karame AT univ DASH lemans DOT fr
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% stephane DOT adjemian AT univ DASH lemans DOT fr
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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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flag = false;
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flag=0 ;
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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/10,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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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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[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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[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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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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tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,ThreadsOptions.local_state_space_iteration_2);
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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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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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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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[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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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 = obs - PredictedObservedMean ;
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StateVectorMean = PredictedStateMean + (CovarianceObservedStateSquareRoot/PredictedObservedVarianceSquareRoot)*Error ;
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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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% Weights = SampleWeights.*sum(weights*probability2(obs,H_lower_triangular_cholesky,tmp(mf1,:)),1) ;
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end
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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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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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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 = obs - PredictedObservedMean ;
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StateVectorMean = PredictedStateMean + KalmanFilterGain*Error ;
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StateVectorVariance = PredictedStateVariance - KalmanFilterGain*PredictedObservedVariance*KalmanFilterGain';
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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 = reduced_rank_cholesky(StateVectorVariance)';%chol(StateVectorVariance + eye(number_of_state_variables)*1e-6)' ;
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[StateVectorVarianceSquareRoot,p] = chol(StateVectorVariance,'lower') ;
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[StateVectorVarianceSquareRoot, p] = chol(StateVectorVariance, 'lower') ;
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if p
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flag=1;
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ProposalStateVector = zeros(number_of_state_variables,1) ;
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Weights = 0.0 ;
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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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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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% Weights = SampleWeights.*sum(probability2(obs,H_lower_triangular_cholesky,tmp(mf1,:))*weights) ;
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end
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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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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 = reduced_rank_cholesky(PredictedStateVariance)';%chol(PredictedStateVariance + eye(number_of_state_variables)*1e-6)' ;
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[PredictedStateVarianceSquareRoot,p] = chol(PredictedStateVariance,'lower') ;
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[PredictedStateVarianceSquareRoot, p] = chol(PredictedStateVariance, 'lower');
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if p
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flag=1;
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ProposalStateVector = zeros(number_of_state_variables,1) ;
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Weights = 0.0 ;
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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(obs,H_lower_triangular_cholesky,measurement_equations(ProposalStateVector,ReducedForm,ThreadsOptions)) ;
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Weights = SampleWeights.*Likelihood.*(Prior./Posterior) ;
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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, DynareOptions, Model));
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Weights = SampleWeights.*Likelihood.*(Prior./Posterior);
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end
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@ -1,7 +1,22 @@
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function [LIK,lik] = conditional_particle_filter(ReducedForm,Y,start,ParticleOptions,ThreadsOptions)
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%
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function [LIK,lik] = conditional_particle_filter(ReducedForm, Y, s, ParticleOptions, ThreadsOptions, DynareOptions, Model)
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% Evaluates the likelihood of a non-linear model with a particle filter
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% - the proposal is built using the Kalman updating step for each particle.
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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×T matrix of (detrended) data, where p is the number of observed variables.
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% - s [integer] scalar, likelihood evaluation starts at s (has to be smaller than T, the sample length provided in Y).
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% - ParticlesOptions [struct]
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% - ThreadsOptions [struct]
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% - DynareOptions [struct]
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% - Model [struct]
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%
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% OUTPUTS
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% - LIK [double] scalar, likelihood
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% - lik [double] (T-s+1)×1 vector, density of observations in each period.
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%
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% REMARKS
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% - The proposal is built using the Kalman updating step for each particle.
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% - we need draws in the errors distributions
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% Whether we use Monte-Carlo draws from a multivariate gaussian distribution
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% as in Amisano & Tristani (JEDC 2010).
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@ -19,25 +34,8 @@ function [LIK,lik] = conditional_particle_filter(ReducedForm,Y,start,ParticleOpt
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% - The use of the Kalman updating step may biais the proposal distribution since
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% it has been derived in a linear context and is implemented in a nonlinear
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% context. That is why particle resampling is performed.
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%
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% INPUTS
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% reduced_form_model [structure] Matlab's structure describing the reduced form model.
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% reduced_form_model.measurement.H [double] (pp x pp) variance matrix of measurement errors.
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% reduced_form_model.state.Q [double] (qq x qq) variance matrix of state errors.
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% reduced_form_model.state.dr [structure] output of resol.m.
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% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
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% start [integer] scalar, likelihood evaluation starts at 'start'.
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% smolyak_accuracy [integer] scalar.
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%
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% OUTPUTS
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% LIK [double] scalar, likelihood
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% lik [double] vector, density of observations in each period.
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%
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% REFERENCES
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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) 2009-2020 Dynare Team
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%
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% This file is part of Dynare.
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%
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@ -54,26 +52,14 @@ function [LIK,lik] = conditional_particle_filter(ReducedForm,Y,start,ParticleOpt
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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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% AUTHOR(S) frederic DOT karame AT univ DASH lemans DOT fr
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% stephane DOT adjemian AT univ DASH lemans DOT fr
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persistent init_flag mf1
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persistent number_of_particles
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persistent sample_size 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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% Set default for third input argument.
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if isempty(s)
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s = 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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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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init_flag = 1;
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number_of_particles = ParticleOptions.number_of_particles ;
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end
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T = size(Y,2);
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p = length(ReducedForm.mf1);
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n = ParticleOptions.number_of_particles;
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% Get covariance matrices
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Q = ReducedForm.Q;
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@ -88,39 +74,37 @@ end
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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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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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normconst2 = sqrt( ((2*pi)^number_of_observed_variables)*prod(det(H)) ) ;
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lik = NaN(sample_size,1);
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LIK = NaN;
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ks = 0 ;
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StateParticles = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean);
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SampleWeights = ones(1,number_of_particles)/number_of_particles ;
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for t=1:sample_size
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obs=Y(:,t);
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flag = zeros(number_of_particles) ;
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parfor i=1:number_of_particles
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[StateParticles(:,i),SampleWeights(i),flag(i)] = ...
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conditional_filter_proposal(ReducedForm,obs,StateParticles(:,i),SampleWeights(i),Q_lower_triangular_cholesky,H_lower_triangular_cholesky,H,ParticleOptions,ThreadsOptions,normconst2) ;
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lik = NaN(T, 1);
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ks = 0;
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StateParticles = bsxfun(@plus, StateVectorVarianceSquareRoot*randn(state_variance_rank, n), StateVectorMean);
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SampleWeights = ones(1, n)/n;
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for t=1:T
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flags = false(n, 1);
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for i=1:n
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[StateParticles(:,i), SampleWeights(i), flags(i)] = ...
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conditional_filter_proposal(ReducedForm, Y(:,t), StateParticles(:,i), SampleWeights(i), Q_lower_triangular_cholesky, H_lower_triangular_cholesky, H, ParticleOptions, ThreadsOptions, DynareOptions, Model);
|
||||
end
|
||||
if sum(flag)~=0
|
||||
LIK=-Inf;
|
||||
lik(t)=-Inf;
|
||||
return
|
||||
end
|
||||
SumSampleWeights = sum(SampleWeights) ;
|
||||
lik(t) = log(SumSampleWeights) ;
|
||||
SampleWeights = SampleWeights./SumSampleWeights ;
|
||||
if (ParticleOptions.resampling.status.generic && neff(SampleWeights)<ParticleOptions.resampling.threshold*sample_size) || ParticleOptions.resampling.status.systematic
|
||||
ks = ks + 1 ;
|
||||
StateParticles = resample(StateParticles',SampleWeights',ParticleOptions)';
|
||||
SampleWeights = ones(1,number_of_particles)/number_of_particles ;
|
||||
if any(flags)
|
||||
LIK = -Inf;
|
||||
lik(t) = -Inf;
|
||||
return
|
||||
end
|
||||
SumSampleWeights = sum(SampleWeights);
|
||||
lik(t) = log(SumSampleWeights);
|
||||
SampleWeights = SampleWeights./SumSampleWeights;
|
||||
if (ParticleOptions.resampling.status.generic && neff(SampleWeights)<ParticleOptions.resampling.threshold*T) || ParticleOptions.resampling.status.systematic
|
||||
ks = ks + 1;
|
||||
StateParticles = resample(StateParticles', SampleWeights', ParticleOptions)';
|
||||
SampleWeights = ones(1, n)/n;
|
||||
end
|
||||
end
|
||||
|
||||
LIK = -sum(lik(start:end));
|
||||
LIK = -sum(lik(s:end));
|
Loading…
Reference in New Issue