126 lines
5.1 KiB
Matlab
126 lines
5.1 KiB
Matlab
function [LIK,lik] = conditional_particle_filter(ReducedForm,Y,start,ParticleOptions,ThreadsOptions)
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%
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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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% - 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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% Whether we use multidimensional Gaussian sparse grids approximations:
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% - a univariate Kronrod-Paterson Gaussian quadrature combined by the Smolyak
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% operator (ref: Winschel & Kratzig, 2010).
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% - a spherical-radial cubature (ref: Arasaratnam & Haykin, 2009a,2009b).
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% - a scaled unscented transform cubature (ref: Julier & Uhlmann 1997, van der
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% Merwe & Wan 2003).
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%
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% Pros:
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% - Allows using current observable information in the proposal
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% - The use of sparse grids Gaussian approximation is much faster than the Monte-Carlo approach
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% Cons:
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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) 2009-2010 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 <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 mf0 mf1
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persistent 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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init_flag = 1;
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number_of_particles = ParticleOptions.number_of_particles ;
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end
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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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if isempty(H)
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H = 0;
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H_lower_triangular_cholesky = 0;
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else
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H_lower_triangular_cholesky = reduced_rank_cholesky(H)';
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end
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% Get initial condition for the state vector.
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StateVectorMean = ReducedForm.StateVectorMean;
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StateVectorVarianceSquareRoot = reduced_rank_cholesky(ReducedForm.StateVectorVariance)';
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state_variance_rank = size(StateVectorVarianceSquareRoot,2);
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Q_lower_triangular_cholesky = reduced_rank_cholesky(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 = log(2*pi)*number_of_observed_variables*prod(diag(H_lower_triangular_cholesky)) ;
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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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for i=1:number_of_particles
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[StateParticles(:,i),SampleWeights(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,normconst2) ;
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end
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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 (ParticleOptions.resampling.status.generic && neff(SampleWeights)<ParticleOptions.resampling.threshold*sample_size) || ParticleOptions.resampling.status.systematic
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ks = ks + 1 ;
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StateParticles = resample(StateParticles',SampleWeights',ParticleOptions)';
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SampleWeights = ones(1,number_of_particles)/number_of_particles ;
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end
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end
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LIK = -sum(lik(start:end));
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