Added new routine for non linear filter (auxiliary particle filter).

matlab/particle/auxiliary_particle_filter.m

+function [LIK,lik] = auxiliary_particle_filter(ReducedForm,Y,start,DynareOptions)
+% Evaluates the likelihood of a nonlinear model with a particle filter allowing eventually resampling.
+%
+% INPUTS
+%    ReducedForm     [structure] Matlab's structure describing the reduced form model.
+%                                       ReducedForm.measurement.H   [double]   (pp x pp) variance matrix of measurement errors.
+%                                       ReducedForm.state.Q         [double]   (qq x qq) variance matrix of state errors.
+%                                       ReducedForm.state.dr        [structure] output of resol.m.
+%    Y                      [double]    pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
+%    start                  [integer]   scalar, likelihood evaluation starts at 'start'.
+%    mf                     [integer]   pp*1 vector of indices.
+%    number_of_particles    [integer]   scalar.
+%
+% OUTPUTS
+%    LIK        [double]    scalar, likelihood
+%    lik        [double]    vector, density of observations in each period.
+%
+% REFERENCES
+%
+% NOTES
+%   The vector "lik" is used to evaluate the jacobian of the likelihood.
+
+% Copyright (C) 2009-2010 Dynare Team
+%
+% This file is part of Dynare.
+%
+% Dynare is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+%
+% Dynare is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with Dynare.  If not, see <http://www.gnu.org/licenses/>.
+persistent init_flag mf0 mf1 number_of_particles
+persistent sample_size number_of_observed_variables number_of_structural_innovations
+
+% Set default
+if isempty(start)
+    start = 1;
+end
+
+% Get steady state and mean.
+steadystate = ReducedForm.steadystate;
+constant = ReducedForm.constant;
+state_variables_steady_state = ReducedForm.state_variables_steady_state;
+
+% Set persistent variables.
+if isempty(init_flag)
+    mf0 = ReducedForm.mf0;
+    mf1 = ReducedForm.mf1;
+    sample_size = size(Y,2);
+    number_of_observed_variables = length(mf1);
+    number_of_structural_innovations = length(ReducedForm.Q);
+    number_of_particles = DynareOptions.particle_filter.number_of_particles;
+    init_flag = 1;
+end
+
+% Set local state space model (first order approximation).
+ghx  = ReducedForm.ghx;
+ghu  = ReducedForm.ghu;
+% Set local state space model (second order approximation).
+ghxx = ReducedForm.ghxx;
+ghuu = ReducedForm.ghuu;
+ghxu = ReducedForm.ghxu;
+
+% Get covariance matrices
+Q = ReducedForm.Q;
+H = ReducedForm.H;
+if isempty(H)
+    H = 0;
+end
+
+% Get initial condition for the state vector.
+StateVectorMean = ReducedForm.StateVectorMean;
+StateVectorVarianceSquareRoot = reduced_rank_cholesky(ReducedForm.StateVectorVariance)';
+state_variance_rank = size(StateVectorVarianceSquareRoot,2);
+Q_lower_triangular_cholesky = chol(Q)';
+
+% Set seed for randn().
+stream=RandStream('mt19937ar','Seed',1);
+RandStream.setDefaultStream(stream);
+
+% Initialization of the likelihood.
+const_lik = log(2*pi)*number_of_observed_variables;
+lik  = NaN(sample_size,1);
+LIK  = NaN;
+
+% Initialization of the weights across particles.
+weights = ones(1,number_of_particles);
+StateVectors = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean);
+for t=1:sample_size
+    yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
+    tmp = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,number_of_particles),ghx,ghu,constant,ghxx,ghuu,ghxu);
+    PredictedObservedMean = mean(tmp(mf1,:),2);
+    PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:));
+    dPredictedObservedMean = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean);
+    PredictedObservedVariance = (dPredictedObservedMean*dPredictedObservedMean')/number_of_particles+H;
+    wtilde = exp(-.5*(const_lik+log(det(PredictedObservedVariance))+sum(PredictionError.*(PredictedObservedVariance\PredictionError),1))) ;
+    tau_tilde = weights.*wtilde ;
+    sum_tau_tilde = sum(tau_tilde) ;
+    lik(t) = log(sum_tau_tilde) ;
+    tau_tilde = tau_tilde/sum_tau_tilde;
+    indx_resmpl = resample(tau_tilde) ;
+    yhat = yhat(:,indx_resmpl) ;
+    wtilde = wtilde(indx_resmpl) ;
+    epsilon = Q_lower_triangular_cholesky*randn(number_of_structural_innovations,number_of_particles);
+    tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu);
+    StateVectors = tmp(mf0,:) ;
+    PredictedObservedMean = mean(tmp(mf1,:),2);
+    PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:));
+    dPredictedObservedMean = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean);
+    PredictedObservedVariance = (dPredictedObservedMean*dPredictedObservedMean')/number_of_particles+H;
+    lnw = exp(-.5*(const_lik+log(det(PredictedObservedVariance))+sum(PredictionError.*(PredictedObservedVariance\PredictionError),1))) ;
+    wtilde = lnw./wtilde;
+    weights = wtilde/sum(wtilde);
+end
+
+LIK = -sum(lik(start:end));
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