147 lines
7.2 KiB
Matlab
147 lines
7.2 KiB
Matlab
function [StateMuPrior,StateSqrtPPrior,StateWeightsPrior,StateMuPost,StateSqrtPPost,StateWeightsPost] =...
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gaussian_mixture_filter_bank(ReducedForm, obs, StateMu, StateSqrtP, StateWeights, ...
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StructuralShocksMu, StructuralShocksSqrtP, StructuralShocksWeights, ...
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ObservationShocksWeights, H, H_lower_triangular_cholesky, normfactO, ...
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ParticleOptions, ThreadsOptions, options_, M_)
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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 © 2009-2022 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 <https://www.gnu.org/licenses/>.
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order = options_.order;
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if ReducedForm.use_k_order_solver
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dr = ReducedForm.dr;
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udr = ReducedForm.udr;
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else
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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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ghs2 = ReducedForm.ghs2;
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if order == 3
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% Set local state space model (third order approximation).
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ghxxx = ReducedForm.ghxxx;
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ghuuu = ReducedForm.ghuuu;
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ghxxu = ReducedForm.ghxxu;
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ghxuu = ReducedForm.ghxuu;
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ghxss = ReducedForm.ghxss;
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ghuss = ReducedForm.ghuss;
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end
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end
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constant = ReducedForm.constant;
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steadystate = ReducedForm.steadystate;
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state_variables_steady_state = ReducedForm.state_variables_steady_state;
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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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numb = number_of_state_variables+number_of_structural_innovations;
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if ParticleOptions.proposal_approximation.cubature
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[nodes3, weights3] = spherical_radial_sigma_points(numb);
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weights_c3 = weights3;
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elseif ParticleOptions.proposal_approximation.unscented
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[nodes3, weights3, weights_c3] = unscented_sigma_points(numb, ParticleOptions);
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else
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error('This approximation for the proposal is unknown!')
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end
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epsilon = bsxfun(@plus, StructuralShocksSqrtP*nodes3(:,number_of_state_variables+1:number_of_state_variables+number_of_structural_innovations)', StructuralShocksMu);
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StateVectors = bsxfun(@plus, StateSqrtP*nodes3(:,1:number_of_state_variables)', StateMu);
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yhat = bsxfun(@minus, StateVectors, state_variables_steady_state);
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if ReducedForm.use_k_order_solver
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tmp = local_state_space_iteration_k(yhat, epsilon, dr, M_, options_, udr);
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else
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if order == 2
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tmp = local_state_space_iteration_2(yhat, epsilon, ghx, ghu, constant, ghxx, ghuu, ghxu, ThreadsOptions.local_state_space_iteration_2);
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elseif order == 3
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tmp = local_state_space_iteration_3(yhat, epsilon, ghx, ghu, ghxx, ghuu, ghxu, ghs2, ghxxx, ghuuu, ghxxu, ghxuu, ghxss, ghuss, steadystate, ThreadsOptions.local_state_space_iteration_3, false);
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else
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error('Order > 3: use_k_order_solver should be set to true');
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end
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end
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PredictedStateMean = tmp(mf0,:)*weights3;
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PredictedObservedMean = tmp(mf1,:)*weights3;
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if ParticleOptions.proposal_approximation.cubature
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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(weights3);
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dObserved = (bsxfun(@minus, tmp(mf1,:), PredictedObservedMean)').*sqrt(weights3);
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PredictedStateVariance = 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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[~, mat] = qr2(big_mat, 0);
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mat = mat';
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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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iPredictedObservedVarianceSquareRoot = inv(PredictedObservedVarianceSquareRoot);
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iPredictedObservedVariance = iPredictedObservedVarianceSquareRoot'*iPredictedObservedVarianceSquareRoot;
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sqrdet = 1/sqrt(det(iPredictedObservedVariance));
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PredictionError = obs - PredictedObservedMean;
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StateVectorMean = PredictedStateMean + CovarianceObservedStateSquareRoot*iPredictedObservedVarianceSquareRoot*PredictionError;
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else
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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_c3)*dState';
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PredictedObservedVariance = dObserved*diag(weights_c3)*dObserved' + H;
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PredictedStateAndObservedCovariance = dState*diag(weights_c3)*dObserved';
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sqrdet = sqrt(det(PredictedObservedVariance));
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iPredictedObservedVariance = inv(PredictedObservedVariance);
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PredictionError = obs - PredictedObservedMean;
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KalmanFilterGain = PredictedStateAndObservedCovariance*iPredictedObservedVariance;
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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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data_lik_GM_g = exp(-0.5*PredictionError'*iPredictedObservedVariance*PredictionError)/abs(normfactO*sqrdet) + 1e-99;
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StateMuPrior = PredictedStateMean;
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StateSqrtPPrior = reduced_rank_cholesky(PredictedStateVariance)';
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StateWeightsPrior = StateWeights*StructuralShocksWeights;
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StateMuPost = StateVectorMean;
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StateSqrtPPost = StateVectorVarianceSquareRoot;
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StateWeightsPost = StateWeightsPrior*ObservationShocksWeights*data_lik_GM_g;
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