2012-01-07 00:10:14 +01:00
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function [LIK,lik] = sequential_importance_particle_filter(ReducedForm,Y,start,DynareOptions)
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% Evaluates the likelihood of a nonlinear model with a particle filter (optionally with resampling).
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2013-04-12 10:29:45 +02:00
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% Standard Sequential Monte Carlo approach with
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% - the usual proposal (the state transition distribution)
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% - options on resampling: none, adaptive or systematic
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2012-01-07 00:10:14 +01:00
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%@info:
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%! @deftypefn {Function File} {@var{y}, @var{y_} =} sequential_importance_particle_filter (@var{ReducedForm},@var{Y}, @var{start}, @var{DynareOptions})
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%! @anchor{particle/sequential_importance_particle_filter}
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%! @sp 1
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2012-03-03 15:50:40 +01:00
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%! Evaluates the likelihood of a nonlinear model with a particle filter (optionally with resampling).
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2012-01-07 00:10:14 +01:00
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%!
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%! @sp 2
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%! @strong{Inputs}
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%! @sp 1
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%! @table @ @var
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%! @item ReducedForm
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%! Structure describing the state space model (built in @ref{non_linear_dsge_likelihood}).
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%! @item Y
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2012-03-03 15:50:40 +01:00
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%! p*smpl matrix of doubles (p is the number of observed variables), the (detrended) data.
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2012-01-07 00:10:14 +01:00
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%! @item start
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%! Integer scalar, likelihood evaluation starts at observation 'start'.
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%! @item DynareOptions
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%! Structure specifying Dynare's options.
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%! @end table
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%! @sp 2
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%! @strong{Outputs}
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%! @sp 1
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%! @table @ @var
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%! @item LIK
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%! double scalar, value of (minus) the logged likelihood.
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%! @item lik
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%! smpl*1 vector of doubles, density of the observations at each period.
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%! @end table
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%! @sp 2
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%! @strong{This function is called by:}
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%! @ref{non_linear_dsge_likelihood}
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%! @sp 2
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%! @strong{This function calls:}
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%!
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%! @end deftypefn
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%@eod:
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2013-02-15 11:58:30 +01:00
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% Copyright (C) 2011-2013 Dynare Team
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2012-01-07 00:10:14 +01:00
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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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2012-11-16 11:57:21 +01:00
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% AUTHOR(S) frederic DOT karame AT univ DASH lemans DOT fr
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2012-03-03 15:50:40 +01:00
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% stephane DOT adjemian AT univ DASH lemans DOT fr
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2012-01-07 00:10:14 +01:00
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2012-03-03 15:50:40 +01:00
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persistent init_flag
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persistent mf0 mf1
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2013-01-28 15:02:15 +01:00
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persistent number_of_particles number_of_state_variables
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2012-01-07 00:10:14 +01:00
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persistent sample_size number_of_observed_variables number_of_structural_innovations
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% Set default value for start
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if isempty(start)
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start = 1;
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end
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2012-11-07 15:58:56 +01:00
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% Set flag for prunning
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pruning = DynareOptions.particle.pruning;
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2012-01-07 00:10:14 +01:00
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% Get steady state and mean.
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2012-11-16 13:12:21 +01:00
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steadystate = ReducedForm.steadystate;
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2012-01-07 00:10:14 +01:00
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constant = ReducedForm.constant;
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state_variables_steady_state = ReducedForm.state_variables_steady_state;
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2012-03-03 15:50:40 +01:00
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% Set persistent variables (if needed).
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2012-01-07 00:10:14 +01:00
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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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2013-01-28 15:02:15 +01:00
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number_of_state_variables = length(mf0);
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2012-01-07 00:10:14 +01:00
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number_of_observed_variables = length(mf1);
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2012-03-03 15:50:40 +01:00
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number_of_structural_innovations = length(ReducedForm.Q);
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2012-01-07 00:10:14 +01:00
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number_of_particles = DynareOptions.particle.number_of_particles;
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init_flag = 1;
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end
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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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2012-03-03 15:50:40 +01:00
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% Get covariance matrices.
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2013-02-05 10:32:20 +01:00
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Q = ReducedForm.Q; % Covariance matrix of the structural innovations.
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2013-06-20 11:55:33 +02:00
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H = ReducedForm.H; % Covariance matrix of the measurement errors.
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2012-01-07 00:10:14 +01:00
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if isempty(H)
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H = 0;
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end
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2012-11-16 11:57:21 +01:00
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% Initialization of the likelihood.
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const_lik = log(2*pi)*number_of_observed_variables;
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lik = NaN(sample_size,1);
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2012-01-07 00:10:14 +01:00
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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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2012-11-07 15:58:56 +01:00
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if pruning
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StateVectorMean_ = StateVectorMean;
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StateVectorVarianceSquareRoot_ = StateVectorVarianceSquareRoot;
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end
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% Get the rank of StateVectorVarianceSquareRoot
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2012-01-07 00:10:14 +01:00
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state_variance_rank = size(StateVectorVarianceSquareRoot,2);
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2012-11-07 15:58:56 +01:00
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% Factorize the covariance matrix of the structural innovations
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2012-01-07 00:10:14 +01:00
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Q_lower_triangular_cholesky = chol(Q)';
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% Set seed for randn().
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2012-03-05 14:37:55 +01:00
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set_dynare_seed('default');
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2012-01-07 00:10:14 +01:00
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% Initialization of the weights across particles.
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2012-03-08 16:36:31 +01:00
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weights = ones(1,number_of_particles)/number_of_particles ;
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2012-01-07 00:10:14 +01:00
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StateVectors = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean);
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2012-11-07 15:58:56 +01:00
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if pruning
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StateVectors_ = StateVectors;
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end
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% Loop over observations
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2012-01-07 00:10:14 +01:00
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for t=1:sample_size
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yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
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epsilon = Q_lower_triangular_cholesky*randn(number_of_structural_innovations,number_of_particles);
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2012-11-07 15:58:56 +01:00
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if pruning
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yhat_ = bsxfun(@minus,StateVectors_,state_variables_steady_state);
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[tmp, tmp_] = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,DynareOptions.threads.local_state_space_iteration_2);
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else
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tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
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end
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2012-11-07 10:48:05 +01:00
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PredictedObservedMean = tmp(mf1,:)*transpose(weights);
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2012-01-07 00:10:14 +01:00
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PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:));
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dPredictedObservedMean = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean);
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2012-11-07 15:58:56 +01:00
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PredictedObservedVariance = bsxfun(@times,dPredictedObservedMean,weights)*dPredictedObservedMean' + H;
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2013-06-24 10:01:17 +02:00
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if rcond(PredictedObservedVariance) > 1e-16
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lnw = -.5*(const_lik+log(det(PredictedObservedVariance))+sum(PredictionError.*(PredictedObservedVariance\PredictionError),1));
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else
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LIK = NaN;
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return
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end
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2012-01-07 00:10:14 +01:00
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dfac = max(lnw);
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wtilde = weights.*exp(lnw-dfac);
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2012-03-30 11:21:24 +02:00
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lik(t) = log(sum(wtilde))+dfac;
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2012-01-07 00:10:14 +01:00
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weights = wtilde/sum(wtilde);
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2013-01-28 15:02:15 +01:00
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if (strcmp(DynareOptions.particle.resampling.status,'generic') && neff(weights)<DynareOptions.particle.resampling.neff_threshold*sample_size ) || ...
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strcmp(DynareOptions.particle.resampling.status,'systematic')
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2012-11-07 15:58:56 +01:00
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if pruning
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2013-06-24 09:59:32 +02:00
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temp = resample([tmp(mf0,:)' tmp_(mf0,:)'],weights',DynareOptions);
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StateVectors = temp(:,1:number_of_state_variables)';
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2013-01-28 15:02:15 +01:00
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StateVectors_ = temp(:,number_of_state_variables+1:2*number_of_state_variables)';
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else
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2013-06-18 16:15:16 +02:00
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StateVectors = resample(tmp(mf0,:)',weights',DynareOptions)';
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2012-11-07 15:58:56 +01:00
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end
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2012-03-30 11:47:24 +02:00
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weights = ones(1,number_of_particles)/number_of_particles;
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2012-03-30 11:48:23 +02:00
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elseif strcmp(DynareOptions.particle.resampling.status,'none')
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2012-01-07 00:10:14 +01:00
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StateVectors = tmp(mf0,:);
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2012-11-07 15:58:56 +01:00
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if pruning
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2012-11-16 13:25:41 +01:00
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StateVectors_ = tmp_(mf0,:);
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2012-11-07 15:58:56 +01:00
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end
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2012-01-07 00:10:14 +01:00
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end
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end
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2013-04-12 10:26:54 +02:00
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LIK = -sum(lik(start:end));
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