127 lines
6.9 KiB
Matlab
127 lines
6.9 KiB
Matlab
function [PredictedStateMean,PredictedStateVarianceSquareRoot,StateVectorMean,StateVectorVarianceSquareRoot] = gaussian_filter_bank(ReducedForm,obs,StateVectorMean,StateVectorVarianceSquareRoot,Q_lower_triangular_cholesky,H_lower_triangular_cholesky,H,DynareOptions)
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%
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% Computes the proposal with a gaussian approximation for importance
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% sampling
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% This proposal is a gaussian distribution calculated à la Kalman
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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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%
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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) 2009-2012 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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persistent init_flag2 mf0 mf1
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persistent number_of_state_variables number_of_observed_variables
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persistent number_of_structural_innovations
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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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if any(any(isnan(ghx))) || any(any(isnan(ghu))) || any(any(isnan(ghxx))) || any(any(isnan(ghuu))) || any(any(isnan(ghxu))) || ...
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any(any(isinf(ghx))) || any(any(isinf(ghu))) || any(any(isinf(ghxx))) || any(any(isinf(ghuu))) || any(any(isinf(ghxu))) ...
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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))
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ghx
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ghu
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ghxx
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ghuu
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ghxu
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end
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constant = ReducedForm.constant;
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state_variables_steady_state = ReducedForm.state_variables_steady_state;
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% Set persistent variables.
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if isempty(init_flag2)
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mf0 = ReducedForm.mf0;
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mf1 = ReducedForm.mf1;
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number_of_state_variables = length(mf0);
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number_of_observed_variables = length(mf1);
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number_of_structural_innovations = length(ReducedForm.Q);
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init_flag2 = 1;
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end
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if strcmpi(DynareOptions.particle.IS_approximation_method,'cubature') || strcmpi(DynareOptions.particle.IS_approximation_method,'monte-carlo')
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[nodes,weights] = spherical_radial_sigma_points(number_of_state_variables+number_of_structural_innovations) ;
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weights_c = weights ;
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end
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if strcmpi(DynareOptions.particle.IS_approximation_method,'quadrature')
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[nodes,weights] = nwspgr('GQN',number_of_state_variables+number_of_structural_innovations,DynareOptions.particle.smolyak_accuracy) ;
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weights_c = weights ;
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end
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if strcmpi(DynareOptions.particle.IS_approximation_method,'unscented')
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[nodes,weights,weights_c] = unscented_sigma_points(number_of_state_variables+number_of_structural_innovations,DynareOptions) ;
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end
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xbar = [StateVectorMean ; zeros(number_of_structural_innovations,1) ] ;
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sqr_Px = [ [ StateVectorVarianceSquareRoot zeros(number_of_state_variables,number_of_structural_innovations) ] ;
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[ zeros(number_of_structural_innovations,number_of_state_variables) Q_lower_triangular_cholesky ] ] ;
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sigma_points = bsxfun(@plus,xbar,sqr_Px*(nodes')) ;
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StateVectors = sigma_points(1:number_of_state_variables,:) ;
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epsilon = sigma_points(number_of_state_variables+1:number_of_state_variables+number_of_structural_innovations,:) ;
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yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
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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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PredictedStateMean = tmp(mf0,:)*weights ;
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PredictedObservedMean = tmp(mf1,:)*weights;
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if strcmpi(DynareOptions.particle.IS_approximation_method,'cubature') || strcmpi(DynareOptions.particle.IS_approximation_method,'monte-carlo')
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PredictedStateMean = sum(PredictedStateMean,2) ;
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PredictedObservedMean = sum(PredictedObservedMean,2) ;
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dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean)'.*sqrt(weights) ;
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dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean)'.*sqrt(weights);
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PredictedStateVarianceSquareRoot = chol(dState'*dState)';
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big_mat = [dObserved dState ; [H_lower_triangular_cholesky zeros(number_of_observed_variables,number_of_state_variables)] ] ;
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[mat1,mat] = qr2(big_mat,0) ;
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mat = mat' ;
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clear('mat1');
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PredictedObservedVarianceSquareRoot = mat(1:number_of_observed_variables,1:number_of_observed_variables) ;
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CovarianceObservedStateSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),1:number_of_observed_variables) ;
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StateVectorVarianceSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),number_of_observed_variables+(1:number_of_state_variables)) ;
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PredictionError = obs - PredictedObservedMean ;
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StateVectorMean = PredictedStateMean + (CovarianceObservedStateSquareRoot/PredictedObservedVarianceSquareRoot)*PredictionError ;
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end
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if strcmpi(DynareOptions.particle.IS_approximation_method,'quadrature') || strcmpi(DynareOptions.particle.IS_approximation_method,'unscented')
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dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean);
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dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean);
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PredictedStateVariance = dState*diag(weights_c)*dState';
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PredictedObservedVariance = dObserved*diag(weights_c)*dObserved' + H;
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PredictedStateAndObservedCovariance = dState*diag(weights_c)*dObserved';
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PredictedStateVarianceSquareRoot = chol(PredictedStateVariance)';
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PredictionError = obs - PredictedObservedMean;
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KalmanFilterGain = PredictedStateAndObservedCovariance/PredictedObservedVariance ;
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StateVectorMean = PredictedStateMean + KalmanFilterGain*PredictionError;
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StateVectorVariance = PredictedStateVariance - KalmanFilterGain*PredictedObservedVariance*KalmanFilterGain';
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StateVectorVariance = .5*(StateVectorVariance+StateVectorVariance');
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StateVectorVarianceSquareRoot = reduced_rank_cholesky(StateVectorVariance)';
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end
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