117 lines
4.4 KiB
Matlab
117 lines
4.4 KiB
Matlab
function initial_distribution = auxiliary_initialization(ReducedForm,Y,start,ParticleOptions,ThreadsOptions)
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% Evaluates the likelihood of a nonlinear model with a particle filter allowing eventually resampling.
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% Copyright © 2011-2022 Dynare Team
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%
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% This file is part of Dynare (particles module).
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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 particles module 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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persistent init_flag mf0 mf1 number_of_particles
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persistent number_of_observed_variables number_of_structural_innovations
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% Set default
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if isempty(start)
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start = 1;
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end
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% Set flag for prunning
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%pruning = ParticleOptions.pruning;
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% Get steady state and mean.
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%steadystate = ReducedForm.steadystate;
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constant = ReducedForm.constant;
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ss = ReducedForm.ys;
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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_flag)
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mf0 = ReducedForm.mf0;
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mf1 = ReducedForm.mf1;
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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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number_of_particles = ParticleOptions.number_of_particles;
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init_flag = 1;
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end
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order = DynareOptions.order;
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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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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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% Get covariance matrices
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Q = ReducedForm.Q;
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H = ReducedForm.H;
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if isempty(H)
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H = 0;
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end
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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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state_variance_rank = size(StateVectorVarianceSquareRoot,2);
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%Q_lower_triangular_cholesky = chol(Q)';
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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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% Set seed for randn().
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set_dynare_seed('default');
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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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% Initialization of the weights across particles.
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weights = ones(1,number_of_particles)/number_of_particles ;
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StateVectors = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean);
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%if pruning
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% StateVectors_ = StateVectors;
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%end
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yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
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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,zeros(number_of_structural_innovations,number_of_particles),ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,ThreadsOptions.local_state_space_iteration_2);
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%else
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if (order == 2)
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tmp = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,number_of_particles),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, zeros(number_of_structural_innovations,number_of_particles), ghx, ghu, ghxx, ghuu, ghxu, ghs2, ghxxx, ghuuu, ghxxu, ghxuu, ghxss, ghuss, ss, options_.threads.local_state_space_iteration_3, false);
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else
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error('Orders > 3 not allowed');
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end
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%end
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PredictedObservedMean = weights*(tmp(mf1,:)');
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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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PredictedObservedVariance = bsxfun(@times,weights,dPredictedObservedMean)*dPredictedObservedMean' + H;
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wtilde = exp(-.5*(const_lik+log(det(PredictedObservedVariance))+sum(PredictionError.*(PredictedObservedVariance\PredictionError),1))) ;
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tau_tilde = weights.*wtilde ;
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tau_tilde = tau_tilde/sum(tau_tilde);
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initial_distribution = resample(StateVectors',tau_tilde',ParticleOptions)' ; |