Added sequential importance particle filter routine.

matlab/particle/sequential_importance_particle_filter.m

+function [LIK,lik] = sequential_importance_particle_filter(ReducedForm,Y,start,DynareOptions)
+% Evaluates the likelihood of a nonlinear model with a particle filter (optionally with resampling).
+
+%@info:
+%! @deftypefn {Function File} {@var{y}, @var{y_} =} sequential_importance_particle_filter (@var{ReducedForm},@var{Y}, @var{start}, @var{DynareOptions})
+%! @anchor{particle/sequential_importance_particle_filter}
+%! @sp 1
+%! Evaluates the likelihood of a nonlinear model with a particle filter (optionally with resampling). 
+%!
+%! @sp 2
+%! @strong{Inputs}
+%! @sp 1
+%! @table @ @var
+%! @item ReducedForm
+%! Structure describing the state space model (built in @ref{non_linear_dsge_likelihood}).
+%! @item Y
+%! p*smpl matrix of doubles (p is the number of observed variables), the (detrended) data.  
+%! @item start
+%! Integer scalar, likelihood evaluation starts at observation 'start'.
+%! @item DynareOptions
+%! Structure specifying Dynare's options.
+%! @end table
+%! @sp 2
+%! @strong{Outputs}
+%! @sp 1
+%! @table @ @var
+%! @item LIK
+%! double scalar, value of (minus) the logged likelihood.
+%! @item lik
+%! smpl*1 vector of doubles, density of the observations at each period.
+%! @end table
+%! @sp 2
+%! @strong{This function is called by:}
+%! @ref{non_linear_dsge_likelihood}
+%! @sp 2
+%! @strong{This function calls:}
+%!
+%! @end deftypefn
+%@eod:
+
+% Copyright (C) 2011 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/>.
+
+% AUTHOR(S) frederic DOT karame AT univ DASH evry DOT fr
+%           stephane DOT adjemian AT univ DASH lemans DOT fr    
+
+persistent init_flag 
+persistent mf0 mf1 
+persistent number_of_particles
+persistent sample_size number_of_observed_variables number_of_structural_innovations
+
+% Set default value for start
+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.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);
+
+% Initialization of the weights across particles.
+nb_obs_resamp = 0 ;
+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);
+    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);
+    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 = -.5*(const_lik+log(det(PredictedObservedVariance))+sum(PredictionError.*(PredictedObservedVariance\PredictionError),1));
+    dfac = max(lnw);
+    wtilde = weights.*exp(lnw-dfac);
+    lik(t) = log(mean(wtilde))+dfac;
+    weights = wtilde/sum(wtilde);
+    Neff = 1/(weights*weights');
+    if (Neff<.5*sample_size && ~isempty(strmatch(DynareOptions.particle.resampling,'generic','exact'))) || ~isempty(strmatch(DynareOptions.particle.resampling,'systematic','exact'))
+        nb_obs_resamp = nb_obs_resamp+1 ;
+        StateVectors = tmp(mf0,resample(weights));
+        weights = ones(1,number_of_particles) ;
+    elseif ~isempty(strmatch(DynareOptions.particle_filter.resampling,'none','exact'))
+        StateVectors = tmp(mf0,:);
+        weights = number_of_particles*weights ;
+    end
+end
+
+LIK = -sum(lik(start:end));
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