1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130
|
function [ProposalStateVector,Weights] = conditional_filter_proposal(ReducedForm,obs,StateVectors,SampleWeights,Q_lower_triangular_cholesky,H_lower_triangular_cholesky,H,DynareOptions,normconst2)
%
% Computes the proposal for each past particle using Gaussian approximations
% for the state errors and the Kalman filter
%
% INPUTS
% reduced_form_model [structure] Matlab's structure describing the reduced form model.
% reduced_form_model.measurement.H [double] (pp x pp) variance matrix of measurement errors.
% reduced_form_model.state.Q [double] (qq x qq) variance matrix of state errors.
% reduced_form_model.state.dr [structure] output of resol.m.
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
%
% 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) 2012-2013 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 lemans DOT fr
% stephane DOT adjemian AT univ DASH lemans DOT fr
persistent init_flag2 mf0 mf1
persistent number_of_state_variables number_of_observed_variables
persistent number_of_structural_innovations
% 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;
if any(any(isnan(ghx))) || any(any(isnan(ghu))) || any(any(isnan(ghxx))) || any(any(isnan(ghuu))) || any(any(isnan(ghxu))) || ...
any(any(isinf(ghx))) || any(any(isinf(ghu))) || any(any(isinf(ghxx))) || any(any(isinf(ghuu))) || any(any(isinf(ghxu))) ...
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))
ghx
ghu
ghxx
ghuu
ghxu
end
constant = ReducedForm.constant;
state_variables_steady_state = ReducedForm.state_variables_steady_state;
% Set persistent variables.
if isempty(init_flag2)
mf0 = ReducedForm.mf0;
mf1 = ReducedForm.mf1;
number_of_state_variables = length(mf0);
number_of_observed_variables = length(mf1);
number_of_structural_innovations = length(ReducedForm.Q);
init_flag2 = 1;
end
if strcmpi(DynareOptions.particle.IS_approximation_method,'cubature') || strcmpi(DynareOptions.particle.IS_approximation_method,'monte-carlo')
[nodes,weights] = spherical_radial_sigma_points(number_of_structural_innovations) ;
weights_c = weights ;
end
if strcmpi(DynareOptions.particle.IS_approximation_method,'quadrature')
[nodes,weights] = nwspgr('GQN',number_of_structural_innovations,DynareOptions.particle.smolyak_accuracy) ;
weights_c = weights ;
end
if strcmpi(DynareOptions.particle.IS_approximation_method,'unscented')
[nodes,weights,weights_c] = unscented_sigma_points(number_of_structural_innovations,DynareOptions) ;
end
epsilon = Q_lower_triangular_cholesky*(nodes') ;
yhat = repmat(StateVectors-state_variables_steady_state,1,size(epsilon,2)) ;
tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
PredictedStateMean = tmp(mf0,:)*weights ;
PredictedObservedMean = tmp(mf1,:)*weights;
if strcmpi(DynareOptions.particle.IS_approximation_method,'cubature') || ...
strcmpi(DynareOptions.particle.IS_approximation_method,'monte-carlo')
PredictedStateMean = sum(PredictedStateMean,2) ;
PredictedObservedMean = sum(PredictedObservedMean,2) ;
dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean)'.*sqrt(weights) ;
dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean)'.*sqrt(weights);
big_mat = [dObserved dState ; [H_lower_triangular_cholesky zeros(number_of_observed_variables,number_of_state_variables)] ] ;
[mat1,mat] = qr2(big_mat,0) ;
mat = mat' ;
clear('mat1');
PredictedObservedVarianceSquareRoot = mat(1:number_of_observed_variables,1:number_of_observed_variables) ;
CovarianceObservedStateSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),1:number_of_observed_variables) ;
StateVectorVarianceSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),number_of_observed_variables+(1:number_of_state_variables)) ;
StateVectorMean = PredictedStateMean + (CovarianceObservedStateSquareRoot/PredictedObservedVarianceSquareRoot)*(obs - PredictedObservedMean) ;
end
if strcmpi(DynareOptions.particle.IS_approximation_method,'quadrature') || ...
strcmpi(DynareOptions.particle.IS_approximation_method,'unscented')
dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean);
dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean);
PredictedStateVariance = dState*diag(weights_c)*dState';
PredictedObservedVariance = dObserved*diag(weights_c)*dObserved' + H;
PredictedStateAndObservedCovariance = dState*diag(weights_c)*dObserved';
KalmanFilterGain = PredictedStateAndObservedCovariance/PredictedObservedVariance ;
StateVectorMean = PredictedStateMean + KalmanFilterGain*(obs - PredictedObservedMean);
StateVectorVariance = PredictedStateVariance - KalmanFilterGain*PredictedObservedVariance*KalmanFilterGain';
StateVectorVariance = .5*(StateVectorVariance+StateVectorVariance');
StateVectorVarianceSquareRoot = reduced_rank_cholesky(StateVectorVariance)';
end
ProposalStateVector = StateVectorVarianceSquareRoot*randn(size(StateVectorVarianceSquareRoot,2),1)+StateVectorMean ;
ypred = measurement_equations(ProposalStateVector,ReducedForm,DynareOptions) ;
foo = H_lower_triangular_cholesky \ (obs - ypred) ;
likelihood = exp(-0.5*(foo)'*foo)/normconst2 + 1e-99 ;
Weights = SampleWeights.*likelihood ;
|