Updated online filter routines.
- Rewrote doc headers - Changed function signatures - Removed persistent variables - Compute the mode of the particle weights - Return the covariance matrix of the particles in the last period - Various cosmetic changesrm-particles^2
Stéphane Adjemian (Charybdis)
parent
22be3797a8
commit
a0fb5c7348
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@ -1,27 +1,27 @@
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function [xparam,std_param,lb_95,ub_95,median_param] = online_auxiliary_filter(xparam1,DynareDataset,dataset_info,DynareOptions,Model,EstimatedParameters,BayesInfo,bounds,DynareResults)
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function [pmean, pmode, pmedian, pstdev, p025, p975, covariance] = online_auxiliary_filter(xparam1, DynareDataset, DynareOptions, Model, EstimatedParameters, BayesInfo, DynareResults)
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% Liu & West particle filter = auxiliary particle filter including Liu & West filter on parameters.
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%
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% INPUTS
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% ReducedForm [structure] Matlab's structure describing the reduced form model.
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% ReducedForm.measurement.H [double] (pp x pp) variance matrix of measurement errors.
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% ReducedForm.state.Q [double] (qq x qq) variance matrix of state errors.
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% ReducedForm.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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% start [integer] scalar, likelihood evaluation starts at 'start'.
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% mf [integer] pp*1 vector of indices.
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% number_of_particles [integer] scalar.
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% - xparam1 [double] n×1 vector, Initial condition for the estimated parameters.
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% - DynareDataset [dseries] Sample used for estimation.
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% - dataset_info [struct] Description of the sample.
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% - DynareOptions [struct] Option values (options_).
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% - Model [struct] Description of the model (M_).
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% - EstimatedParameters [struct] Description of the estimated parameters (estim_params_).
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% - BayesInfo [struct] Prior definition (bayestopt_).
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% - DynareResults [struct] Results (oo_).
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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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% - pmean [double] n×1 vector, mean of the particles at the end of the sample (for the parameters).
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% - pmode [double] n×1 vector, mode of the particles at the end of the sample (for the parameters).
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% - pmedian [double] n×1 vector, median of the particles at the end of the sample (for the parameters).
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% - pstdev [double] n×1 vector, st. dev. of the particles at the end of the sample (for the parameters).
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% - p025 [double] n×1 vector, 2.5 percent of the particles are below p025(i) for i=1,…,n.
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% - p975 [double] n×1 vector, 97.5 percent of the particles are below p975(i) for i=1,…,n.
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% - covariance [double] n×n matrix, covariance of the particles at the end of the sample.
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% Copyright (C) 2013-2017 Dynare Team
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% Copyright (C) 2013-2019 Dynare Team
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%
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% This file is part of Dynare.
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%
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@ -37,33 +37,27 @@ function [xparam,std_param,lb_95,ub_95,median_param] = online_auxiliary_filter(x
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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 Y init_flag mf0 mf1 number_of_particles number_of_parameters liu_west_delta liu_west_chol_sigma_bar
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persistent start_param sample_size number_of_observed_variables number_of_structural_innovations
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% Set seed for randn().
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set_dynare_seed('default') ;
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set_dynare_seed('default');
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pruning = DynareOptions.particle.pruning;
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second_resample = DynareOptions.particle.resampling.status.systematic ;
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variance_update = 1 ;
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second_resample = DynareOptions.particle.resampling.status.systematic;
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variance_update = true;
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bounds = prior_bounds(BayesInfo, DynareOptions.prior_trunc); % Reset bounds as lb and ub must only be operational during mode-finding
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% initialization of state particles
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[ys,trend_coeff,exit_flag,info,Model,DynareOptions,BayesInfo,DynareResults,ReducedForm] = ...
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solve_model_for_online_filter(1,xparam1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults) ;
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[~, Model, DynareOptions, DynareResults, ReducedForm] = solve_model_for_online_filter(true, xparam1, DynareDataset, DynareOptions, Model, EstimatedParameters, BayesInfo, bounds, DynareResults);
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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_particles = DynareOptions.particle.number_of_particles;
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number_of_parameters = size(xparam1,1) ;
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Y = DynareDataset.data ;
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sample_size = size(Y,1);
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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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liu_west_delta = DynareOptions.particle.liu_west_delta ;
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start_param = xparam1 ;
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init_flag = 1;
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end
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mf0 = ReducedForm.mf0;
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mf1 = ReducedForm.mf1;
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number_of_particles = DynareOptions.particle.number_of_particles;
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number_of_parameters = size(xparam1,1);
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Y = DynareDataset.data;
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sample_size = size(Y,1);
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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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liu_west_delta = DynareOptions.particle.liu_west_delta;
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% Get initial conditions for the state particles
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StateVectorMean = ReducedForm.StateVectorMean;
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@ -75,43 +69,34 @@ if pruning
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end
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% parameters for the Liu & West filter
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small_a = (3*liu_west_delta-1)/(2*liu_west_delta) ;
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b_square = 1-small_a*small_a ;
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small_a = (3*liu_west_delta-1)/(2*liu_west_delta);
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b_square = 1-small_a*small_a;
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% Initialization of parameter particles
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xparam = zeros(number_of_parameters,number_of_particles) ;
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%stderr = sqrt(bsxfun(@power,bounds.ub-bounds.lb,2)/12)/100 ;
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%stderr = sqrt(bsxfun(@power,bounds.ub-bounds.lb,2)/12)/50 ;
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%stderr = sqrt(bsxfun(@power,bounds.ub-bounds.lb,2)/12)/20 ;
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bounds = prior_bounds(BayesInfo,DynareOptions.prior_trunc); %reset bounds as lb and ub must only be operational during mode-finding
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xparam = zeros(number_of_parameters,number_of_particles);
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prior_draw(BayesInfo,DynareOptions.prior_trunc);
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for i=1:number_of_particles
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info = 1;
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while info==1
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%candidate = start_param + .001*liu_west_chol_sigma_bar*randn(number_of_parameters,1) ;
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%candidate = start_param + bsxfun(@times,stderr,randn(number_of_parameters,1)) ;
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info = 12042009;
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while info
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candidate = prior_draw()';
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if all(candidate(:) >= bounds.lb) && all(candidate(:) <= bounds.ub)
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[ys,trend_coeff,exit_flag,info,Model,DynareOptions,BayesInfo,DynareResults,ReducedForm] = ...
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solve_model_for_online_filter(1,candidate(:),DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults) ;
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if info==0
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xparam(:,i) = candidate(:) ;
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end
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end
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[info, Model, DynareOptions, DynareResults] = solve_model_for_online_filter(false, xparam1, DynareDataset, DynareOptions, Model, EstimatedParameters, BayesInfo, bounds, DynareResults);
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if ~info
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xparam(:,i) = candidate(:);
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end
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end
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end
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%xparam = bsxfun(@plus,bounds(:,1),bsxfun(@times,(bounds(:,2)-bounds(:,1)),rand(number_of_parameters,number_of_particles))) ;
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end
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% Initialization of the weights of particles.
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weights = ones(1,number_of_particles)/number_of_particles ;
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weights = ones(1,number_of_particles)/number_of_particles;
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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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mean_xparam = zeros(number_of_parameters,sample_size) ;
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median_xparam = zeros(number_of_parameters,sample_size) ;
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std_xparam = zeros(number_of_parameters,sample_size) ;
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lb95_xparam = zeros(number_of_parameters,sample_size) ;
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ub95_xparam = zeros(number_of_parameters,sample_size) ;
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mean_xparam = zeros(number_of_parameters,sample_size);
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mode_xparam = zeros(number_of_parameters,sample_size);
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median_xparam = zeros(number_of_parameters,sample_size);
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std_xparam = zeros(number_of_parameters,sample_size);
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lb95_xparam = zeros(number_of_parameters,sample_size);
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ub95_xparam = zeros(number_of_parameters,sample_size);
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%% The Online filter
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for t=1:sample_size
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@ -121,20 +106,20 @@ for t=1:sample_size
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fprintf('\nSubsample with only the first observation.\n\n', int2str(t))
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end
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% Moments of parameters particles distribution
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m_bar = xparam*(weights') ;
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temp = bsxfun(@minus,xparam,m_bar) ;
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sigma_bar = (bsxfun(@times,weights,temp))*(temp') ;
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if variance_update==1
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chol_sigma_bar = chol(b_square*sigma_bar)' ;
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m_bar = xparam*(weights');
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temp = bsxfun(@minus,xparam,m_bar);
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sigma_bar = (bsxfun(@times,weights,temp))*(temp');
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if variance_update
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chol_sigma_bar = chol(b_square*sigma_bar)';
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end
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% Prediction (without shocks)
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fore_xparam = bsxfun(@plus,(1-small_a).*m_bar,small_a.*xparam) ;
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tau_tilde = zeros(1,number_of_particles) ;
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fore_xparam = bsxfun(@plus,(1-small_a).*m_bar,small_a.*xparam);
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tau_tilde = zeros(1,number_of_particles);
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for i=1:number_of_particles
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% model resolution
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[ys,trend_coeff,exit_flag,info,Model,DynareOptions,BayesInfo,DynareResults,ReducedForm] = ...
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solve_model_for_online_filter(t,fore_xparam(:,i),DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults) ;
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if info==0
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[info, Model, DynareOptions, DynareResults, ReducedForm] = ...
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solve_model_for_online_filter(false, fore_xparam(:,i), DynareDataset, DynareOptions, Model, EstimatedParameters, BayesInfo, bounds, DynareResults);
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if ~info
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steadystate = ReducedForm.steadystate;
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state_variables_steady_state = ReducedForm.state_variables_steady_state;
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% Set local state space model (second-order approximation).
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@ -148,38 +133,36 @@ for t=1:sample_size
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yhat = bsxfun(@minus,StateVectors(:,i),state_variables_steady_state);
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if pruning
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yhat_ = bsxfun(@minus,StateVectors_(:,i),state_variables_steady_state);
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[tmp, tmp_] = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,1),ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,DynareOptions.threads.local_state_space_iteration_2);
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[tmp, ~] = local_state_space_iteration_2(yhat, zeros(number_of_structural_innovations, 1), 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,zeros(number_of_structural_innovations,1),ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
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tmp = local_state_space_iteration_2(yhat, zeros(number_of_structural_innovations, 1), ghx, ghu, constant, ghxx, ghuu, ghxu, DynareOptions.threads.local_state_space_iteration_2);
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end
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PredictionError = bsxfun(@minus,Y(t,:)',tmp(mf1,:));
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% Replace Gaussian density with a Student density with 3 degrees of
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% freedom for fat tails.
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z = sum(PredictionError.*(ReducedForm.H\PredictionError),1) ;
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tau_tilde(i) = weights(i).*(tpdf(z,3*ones(size(z)))+1e-99) ;
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%tau_tilde(i) = weights(i).*exp(-.5*(const_lik+log(det(ReducedForm.H))+sum(PredictionError.*(ReducedForm.H\PredictionError),1))) ;
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end
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PredictionError = bsxfun(@minus,Y(t,:)', tmp(mf1,:));
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% Replace Gaussian density with a Student density with 3 degrees of freedom for fat tails.
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z = sum(PredictionError.*(ReducedForm.H\PredictionError), 1) ;
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tau_tilde(i) = weights(i).*(tpdf(z, 3*ones(size(z)))+1e-99) ;
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end
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end
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% particles selection
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tau_tilde = tau_tilde/sum(tau_tilde) ;
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indx = resample(0,tau_tilde',DynareOptions.particle);
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StateVectors = StateVectors(:,indx) ;
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xparam = fore_xparam(:,indx);
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tau_tilde = tau_tilde/sum(tau_tilde);
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indx = resample(0, tau_tilde', DynareOptions.particle);
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StateVectors = StateVectors(:,indx);
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xparam = fore_xparam(:,indx);
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if pruning
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StateVectors_ = StateVectors_(:,indx) ;
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StateVectors_ = StateVectors_(:,indx);
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end
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w_stage1 = weights(indx)./tau_tilde(indx) ;
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w_stage1 = weights(indx)./tau_tilde(indx);
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% draw in the new distributions
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wtilde = zeros(1,number_of_particles) ;
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wtilde = zeros(1, number_of_particles);
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for i=1:number_of_particles
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info=1 ;
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while info==1
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candidate = xparam(:,i) + chol_sigma_bar*randn(number_of_parameters,1) ;
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if all(candidate >= bounds.lb) && all(candidate <= bounds.ub)
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% model resolution for new parameters particles
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[ys,trend_coeff,exit_flag,info,Model,DynareOptions,BayesInfo,DynareResults,ReducedForm] = ...
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solve_model_for_online_filter(t,candidate,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults) ;
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if info==0
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info = 12042009;
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while info
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candidate = xparam(:,i) + chol_sigma_bar*randn(number_of_parameters, 1);
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if all(candidate>=bounds.lb) && all(candidate<=bounds.ub)
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% model resolution for new parameters particles
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[info, Model, DynareOptions, DynareResults, ReducedForm] = ...
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solve_model_for_online_filter(false, candidate, DynareDataset, DynareOptions, Model, EstimatedParameters, BayesInfo, bounds, DynareResults) ;
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if ~info
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xparam(:,i) = candidate ;
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steadystate = ReducedForm.steadystate;
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state_variables_steady_state = ReducedForm.state_variables_steady_state;
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@ -191,71 +174,75 @@ for t=1:sample_size
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ghuu = ReducedForm.ghuu;
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ghxu = ReducedForm.ghxu;
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% Get covariance matrices and structural shocks
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epsilon = chol(ReducedForm.Q)'*randn(number_of_structural_innovations,1) ;
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epsilon = chol(ReducedForm.Q)'*randn(number_of_structural_innovations, 1);
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% compute particles likelihood contribution
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yhat = bsxfun(@minus,StateVectors(:,i),state_variables_steady_state);
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yhat = bsxfun(@minus,StateVectors(:,i), state_variables_steady_state);
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if pruning
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yhat_ = bsxfun(@minus,StateVectors_(:,i),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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StateVectors_(:,i) = tmp_(mf0,:) ;
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yhat_ = bsxfun(@minus,StateVectors_(:,i), 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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StateVectors_(:,i) = tmp_(mf0,:);
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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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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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StateVectors(:,i) = tmp(mf0,:) ;
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PredictionError = bsxfun(@minus,Y(t,:)',tmp(mf1,:));
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wtilde(i) = w_stage1(i)*exp(-.5*(const_lik+log(det(ReducedForm.H))+sum(PredictionError.*(ReducedForm.H\PredictionError),1)));
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end
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StateVectors(:,i) = tmp(mf0,:);
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PredictionError = bsxfun(@minus,Y(t,:)', tmp(mf1,:));
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wtilde(i) = w_stage1(i)*exp(-.5*(const_lik+log(det(ReducedForm.H))+sum(PredictionError.*(ReducedForm.H\PredictionError), 1)));
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end
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end
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end
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end
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% normalization
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weights = wtilde/sum(wtilde);
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if (variance_update==1) && (neff(weights)<DynareOptions.particle.resampling.threshold*sample_size)
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variance_update = 0 ;
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if variance_update && (neff(weights)<DynareOptions.particle.resampling.threshold*sample_size)
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variance_update = false;
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end
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% final resampling (not advised)
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if second_resample==1
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indx = resample(0,weights,DynareOptions.particle);
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if second_resample
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[~, idmode] = max(weights);
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mode_xparam(:,t) = xparam(:,idmode);
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indx = resample(0, weights,DynareOptions.particle);
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StateVectors = StateVectors(:,indx) ;
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if pruning
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StateVectors_ = StateVectors_(:,indx) ;
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StateVectors_ = StateVectors_(:,indx);
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end
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xparam = xparam(:,indx) ;
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weights = ones(1,number_of_particles)/number_of_particles ;
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mean_xparam(:,t) = mean(xparam,2);
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mat_var_cov = bsxfun(@minus,xparam,mean_xparam(:,t)) ;
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mat_var_cov = (mat_var_cov*mat_var_cov')/(number_of_particles-1) ;
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std_xparam(:,t) = sqrt(diag(mat_var_cov)) ;
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xparam = xparam(:,indx);
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weights = ones(1, number_of_particles)/number_of_particles;
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mean_xparam(:,t) = mean(xparam, 2);
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mat_var_cov = bsxfun(@minus, xparam, mean_xparam(:,t));
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mat_var_cov = (mat_var_cov*mat_var_cov')/(number_of_particles-1);
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std_xparam(:,t) = sqrt(diag(mat_var_cov));
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for i=1:number_of_parameters
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temp = sortrows(xparam(i,:)') ;
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lb95_xparam(i,t) = temp(0.025*number_of_particles) ;
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median_xparam(i,t) = temp(0.5*number_of_particles) ;
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ub95_xparam(i,t) = temp(0.975*number_of_particles) ;
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temp = sortrows(xparam(i,:)');
|
||||
lb95_xparam(i,t) = temp(0.025*number_of_particles);
|
||||
median_xparam(i,t) = temp(0.5*number_of_particles);
|
||||
ub95_xparam(i,t) = temp(0.975*number_of_particles);
|
||||
end
|
||||
end
|
||||
if second_resample==0
|
||||
mean_xparam(:,t) = xparam*(weights') ;
|
||||
mat_var_cov = bsxfun(@minus,xparam,mean_xparam(:,t)) ;
|
||||
mat_var_cov = mat_var_cov*(bsxfun(@times,mat_var_cov,weights)') ;
|
||||
std_xparam(:,t) = sqrt(diag(mat_var_cov)) ;
|
||||
if second_resample
|
||||
[~, idmode] = max(weights);
|
||||
mode_xparam(:,t) = xparam(:,idmode);
|
||||
mean_xparam(:,t) = xparam*(weights');
|
||||
mat_var_cov = bsxfun(@minus, xparam,mean_xparam(:,t));
|
||||
mat_var_cov = mat_var_cov*(bsxfun(@times, mat_var_cov, weights)');
|
||||
std_xparam(:,t) = sqrt(diag(mat_var_cov));
|
||||
for i=1:number_of_parameters
|
||||
temp = sortrows([xparam(i,:)' weights'],1) ;
|
||||
cumulated_weights = cumsum(temp(:,2)) ;
|
||||
pass1=1 ;
|
||||
pass2=1 ;
|
||||
pass3=1 ;
|
||||
temp = sortrows([xparam(i,:)' weights'], 1);
|
||||
cumulated_weights = cumsum(temp(:,2));
|
||||
pass1 = false;
|
||||
pass2 = false;
|
||||
pass3 = false;
|
||||
for j=1:number_of_particles
|
||||
if cumulated_weights(j)>=0.025 && pass1==1
|
||||
lb95_xparam(i,t) = temp(j,1) ;
|
||||
pass1 = 2 ;
|
||||
if ~pass1 && cumulated_weights(j)>=0.025
|
||||
lb95_xparam(i,t) = temp(j,1);
|
||||
pass1 = true;
|
||||
end
|
||||
if cumulated_weights(j)>=0.5 && pass2==1
|
||||
median_xparam(i,t) = temp(j,1) ;
|
||||
pass2 = 2 ;
|
||||
if ~pass2 && cumulated_weights(j)>=0.5
|
||||
median_xparam(i,t) = temp(j,1);
|
||||
pass2 = true;
|
||||
end
|
||||
if cumulated_weights(j)>=0.975 && pass3==1
|
||||
ub95_xparam(i,t) = temp(j,1) ;
|
||||
pass3 = 2 ;
|
||||
if ~pass3 && cumulated_weights(j)>=0.975
|
||||
ub95_xparam(i,t) = temp(j,1);
|
||||
pass3 = true;
|
||||
end
|
||||
end
|
||||
end
|
||||
|
|
@ -267,22 +254,22 @@ for t=1:sample_size
|
|||
disp([str])
|
||||
disp('')
|
||||
end
|
||||
distrib_param = xparam ;
|
||||
xparam = mean_xparam(:,sample_size) ;
|
||||
std_param = std_xparam(:,sample_size) ;
|
||||
lb_95 = lb95_xparam(:,sample_size) ;
|
||||
ub_95 = ub95_xparam(:,sample_size) ;
|
||||
median_param = median_xparam(:,sample_size) ;
|
||||
|
||||
pmean = xparam(:,sample_size);
|
||||
pmode = mode_xparam(:,sample_size);
|
||||
pstdev = std_xparam(:,sample_size) ;
|
||||
p025 = lb95_xparam(:,sample_size) ;
|
||||
p975 = ub95_xparam(:,sample_size) ;
|
||||
pmedian = median_xparam(:,sample_size) ;
|
||||
covariance = mat_var_cov;
|
||||
|
||||
%% Plot parameters trajectory
|
||||
TeX = DynareOptions.TeX;
|
||||
|
||||
[nbplt,nr,nc,lr,lc,nstar] = pltorg(number_of_parameters);
|
||||
nr = ceil(sqrt(number_of_parameters)) ;
|
||||
nc = floor(sqrt(number_of_parameters));
|
||||
nbplt = 1 ;
|
||||
|
||||
|
||||
if TeX
|
||||
fidTeX = fopen([Model.fname '_param_traj.tex'],'w');
|
||||
fprintf(fidTeX,'%% TeX eps-loader file generated by online_auxiliary_filter.m (Dynare).\n');
|
||||
|
|
@ -290,15 +277,13 @@ if TeX
|
|||
fprintf(fidTeX,' \n');
|
||||
end
|
||||
|
||||
z = 1:1:sample_size ;
|
||||
|
||||
for plt = 1:nbplt,
|
||||
for plt = 1:nbplt
|
||||
if TeX
|
||||
NAMES = [];
|
||||
TeXNAMES = [];
|
||||
end
|
||||
hh = dyn_figure(DynareOptions.nodisplay,'Name','Parameters Trajectories');
|
||||
for k=1:length(xparam)
|
||||
for k=1:length(pmean)
|
||||
subplot(nr,nc,k)
|
||||
[name,texname] = get_the_name(k,TeX,Model,EstimatedParameters,DynareOptions);
|
||||
if TeX
|
||||
|
|
@ -310,15 +295,17 @@ for plt = 1:nbplt,
|
|||
TeXNAMES = char(TeXNAMES,texname);
|
||||
end
|
||||
end
|
||||
y = [mean_xparam(k,:)' median_xparam(k,:)' lb95_xparam(k,:)' ub95_xparam(k,:)' xparam(k)*ones(sample_size,1)] ;
|
||||
plot(z,y);
|
||||
% Draw the surface for an interval containing 95% of the particles.
|
||||
shade(1:sample_size, ub95_xparam(k,:)', 1:sample_size, lb95_xparam(k,:)', 'FillType',[1 2], 'LineStyle', 'none', 'Marker', 'none')
|
||||
hold on
|
||||
% Draw the mean of particles.
|
||||
plot(1:sample_size, mean_xparam(k,:), '-k', 'linewidth', 2)
|
||||
title(name,'interpreter','none')
|
||||
hold off
|
||||
axis tight
|
||||
drawnow
|
||||
end
|
||||
dyn_saveas(hh,[ Model.fname '_param_traj' int2str(plt) ],DynareOptions.nodisplay,DynareOptions.graph_format);
|
||||
dyn_saveas(hh, [Model.fname '_param_traj' int2str(plt)], DynareOptions.nodisplay, DynareOptions.graph_format);
|
||||
if TeX
|
||||
% TeX eps loader file
|
||||
fprintf(fidTeX,'\\begin{figure}[H]\n');
|
||||
|
|
@ -334,17 +321,17 @@ for plt = 1:nbplt,
|
|||
end
|
||||
end
|
||||
|
||||
%% Plot Parameter Densities
|
||||
% Plot Parameter Densities
|
||||
number_of_grid_points = 2^9; % 2^9 = 512 !... Must be a power of two.
|
||||
bandwidth = 0; % Rule of thumb optimal bandwidth parameter.
|
||||
kernel_function = 'gaussian'; % Gaussian kernel for Fast Fourier Transform approximation.
|
||||
for plt = 1:nbplt,
|
||||
for plt = 1:nbplt
|
||||
if TeX
|
||||
NAMES = [];
|
||||
TeXNAMES = [];
|
||||
end
|
||||
hh = dyn_figure(DynareOptions.nodisplay,'Name','Parameters Densities');
|
||||
for k=1:length(xparam)
|
||||
for k=1:length(pmean)
|
||||
subplot(nr,nc,k)
|
||||
[name,texname] = get_the_name(k,TeX,Model,EstimatedParameters,DynareOptions);
|
||||
if TeX
|
||||
|
|
@ -356,12 +343,12 @@ for plt = 1:nbplt,
|
|||
TeXNAMES = char(TeXNAMES,texname);
|
||||
end
|
||||
end
|
||||
optimal_bandwidth = mh_optimal_bandwidth(distrib_param(k,:)',number_of_particles,bandwidth,kernel_function);
|
||||
[density(:,1),density(:,2)] = kernel_density_estimate(distrib_param(k,:)',number_of_grid_points,...
|
||||
number_of_particles,optimal_bandwidth,kernel_function);
|
||||
plot(density(:,1),density(:,2));
|
||||
optimal_bandwidth = mh_optimal_bandwidth(xparam(k,:)',number_of_particles,bandwidth,kernel_function);
|
||||
[density(:,1),density(:,2)] = kernel_density_estimate(xparam(k,:)', number_of_grid_points, ...
|
||||
number_of_particles, optimal_bandwidth, kernel_function);
|
||||
plot(density(:,1), density(:,2));
|
||||
hold on
|
||||
title(name,'interpreter','none')
|
||||
title(name, 'interpreter', 'none')
|
||||
hold off
|
||||
axis tight
|
||||
drawnow
|
||||
|
|
@ -369,9 +356,9 @@ for plt = 1:nbplt,
|
|||
dyn_saveas(hh,[ Model.fname '_param_density' int2str(plt) ],DynareOptions.nodisplay,DynareOptions.graph_format);
|
||||
if TeX
|
||||
% TeX eps loader file
|
||||
fprintf(fidTeX,'\\begin{figure}[H]\n');
|
||||
fprintf(fidTeX, '\\begin{figure}[H]\n');
|
||||
for jj = 1:length(x)
|
||||
fprintf(fidTeX,'\\psfrag{%s}[1][][0.5][0]{%s}\n',deblank(NAMES(jj,:)),deblank(TeXNAMES(jj,:)));
|
||||
fprintf(fidTeX, '\\psfrag{%s}[1][][0.5][0]{%s}\n', deblank(NAMES(jj,:)), deblank(TeXNAMES(jj,:)));
|
||||
end
|
||||
fprintf(fidTeX,'\\centering \n');
|
||||
fprintf(fidTeX,'\\includegraphics[scale=0.5]{%s_ParametersDensities%s}\n',Model.fname,int2str(plt));
|
||||
|
|
|
|||
|
|
@ -1,107 +1,26 @@
|
|||
function [ys,trend_coeff,exit_flag,info,Model,DynareOptions,BayesInfo,DynareResults,ReducedForm] = solve_model_for_online_filter(observation_number,xparam1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults)
|
||||
% solve the dsge model for an particular parameters set.
|
||||
function [info, Model, DynareOptions, DynareResults, ReducedForm] = ...
|
||||
solve_model_for_online_filter(setinitialcondition, xparam1, DynareDataset, DynareOptions, Model, EstimatedParameters, BayesInfo, bounds, DynareResults)
|
||||
|
||||
%@info:
|
||||
%! @deftypefn {Function File} {[@var{fval},@var{exit_flag},@var{ys},@var{trend_coeff},@var{info},@var{Model},@var{DynareOptions},@var{BayesInfo},@var{DynareResults}] =} non_linear_dsge_likelihood (@var{xparam1},@var{DynareDataset},@var{DynareOptions},@var{Model},@var{EstimatedParameters},@var{BayesInfo},@var{DynareResults})
|
||||
%! @anchor{dsge_likelihood}
|
||||
%! @sp 1
|
||||
%! Evaluates the posterior kernel of a dsge model using a non linear filter.
|
||||
%! @sp 2
|
||||
%! @strong{Inputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item xparam1
|
||||
%! Vector of doubles, current values for the estimated parameters.
|
||||
%! @item DynareDataset
|
||||
%! Matlab's structure describing the dataset (initialized by dynare, see @ref{dataset_}).
|
||||
%! @item DynareOptions
|
||||
%! Matlab's structure describing the options (initialized by dynare, see @ref{options_}).
|
||||
%! @item Model
|
||||
%! Matlab's structure describing the Model (initialized by dynare, see @ref{M_}).
|
||||
%! @item EstimatedParamemeters
|
||||
%! Matlab's structure describing the estimated_parameters (initialized by dynare, see @ref{estim_params_}).
|
||||
%! @item BayesInfo
|
||||
%! Matlab's structure describing the priors (initialized by dynare, see @ref{bayesopt_}).
|
||||
%! @item DynareResults
|
||||
%! Matlab's structure gathering the results (initialized by dynare, see @ref{oo_}).
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{Outputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item fval
|
||||
%! Double scalar, value of (minus) the likelihood.
|
||||
%! @item exit_flag
|
||||
%! Integer scalar, equal to zero if the routine return with a penalty (one otherwise).
|
||||
%! @item ys
|
||||
%! Vector of doubles, steady state level for the endogenous variables.
|
||||
%! @item trend_coeffs
|
||||
%! Matrix of doubles, coefficients of the deterministic trend in the measurement equation.
|
||||
%! @item info
|
||||
%! Integer scalar, error code.
|
||||
%! @table @ @code
|
||||
%! @item info==0
|
||||
%! No error.
|
||||
%! @item info==1
|
||||
%! The model doesn't determine the current variables uniquely.
|
||||
%! @item info==2
|
||||
%! MJDGGES returned an error code.
|
||||
%! @item info==3
|
||||
%! Blanchard & Kahn conditions are not satisfied: no stable equilibrium.
|
||||
%! @item info==4
|
||||
%! Blanchard & Kahn conditions are not satisfied: indeterminacy.
|
||||
%! @item info==5
|
||||
%! Blanchard & Kahn conditions are not satisfied: indeterminacy due to rank failure.
|
||||
%! @item info==6
|
||||
%! The jacobian evaluated at the deterministic steady state is complex.
|
||||
%! @item info==19
|
||||
%! The steadystate routine thrown an exception (inconsistent deep parameters).
|
||||
%! @item info==20
|
||||
%! Cannot find the steady state, info(2) contains the sum of square residuals (of the static equations).
|
||||
%! @item info==21
|
||||
%! The steady state is complex, info(2) contains the sum of square of imaginary parts of the steady state.
|
||||
%! @item info==22
|
||||
%! The steady has NaNs.
|
||||
%! @item info==23
|
||||
%! M_.params has been updated in the steadystate routine and has complex valued scalars.
|
||||
%! @item info==24
|
||||
%! M_.params has been updated in the steadystate routine and has some NaNs.
|
||||
%! @item info==30
|
||||
%! Ergodic variance can't be computed.
|
||||
%! @item info==41
|
||||
%! At least one parameter is violating a lower bound condition.
|
||||
%! @item info==42
|
||||
%! At least one parameter is violating an upper bound condition.
|
||||
%! @item info==43
|
||||
%! The covariance matrix of the structural innovations is not positive definite.
|
||||
%! @item info==44
|
||||
%! The covariance matrix of the measurement errors is not positive definite.
|
||||
%! @item info==45
|
||||
%! Likelihood is not a number (NaN).
|
||||
%! @item info==45
|
||||
%! Likelihood is a complex valued number.
|
||||
%! @end table
|
||||
%! @item Model
|
||||
%! Matlab's structure describing the model (initialized by dynare, see @ref{M_}).
|
||||
%! @item DynareOptions
|
||||
%! Matlab's structure describing the options (initialized by dynare, see @ref{options_}).
|
||||
%! @item BayesInfo
|
||||
%! Matlab's structure describing the priors (initialized by dynare, see @ref{bayesopt_}).
|
||||
%! @item DynareResults
|
||||
%! Matlab's structure gathering the results (initialized by dynare, see @ref{oo_}).
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{This function is called by:}
|
||||
%! @sp 1
|
||||
%! @ref{dynare_estimation_1}, @ref{mode_check}
|
||||
%! @sp 2
|
||||
%! @strong{This function calls:}
|
||||
%! @sp 1
|
||||
%! @ref{dynare_resolve}, @ref{lyapunov_symm}, @ref{priordens}
|
||||
%! @end deftypefn
|
||||
%@eod:
|
||||
% Solves the dsge model for an particular parameters set.
|
||||
%
|
||||
% INPUTS
|
||||
% - setinitialcondition [logical] return initial condition if true.
|
||||
% - xparam1 [double] n×1 vector, parameter values.
|
||||
% - DynareDataset [struct] Dataset for estimation (dataset_).
|
||||
% - DynareOptions [struct] Dynare options (options_).
|
||||
% - Model [struct] Model description (M_).
|
||||
% - EstimatedParameters [struct] Estimated parameters (estim_params_).
|
||||
% - BayesInfo [struct] Prior definition (bayestopt_).
|
||||
% - DynareResults [struct] Dynare results (oo_).
|
||||
%
|
||||
% OUTPUTS
|
||||
% - info [integer] scalar, nonzero if any problem occur when computing the reduced form.
|
||||
% - Model [struct] Model description (M_).
|
||||
% - DynareOptions [struct] Dynare options (options_).
|
||||
% - DynareResults [struct] Dynare results (oo_).
|
||||
% - ReducedForm [struct] Reduced form model.
|
||||
|
||||
% Copyright (C) 2013-2017 Dynare Team
|
||||
% Copyright (C) 2013-2019 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
|
|
@ -118,46 +37,25 @@ function [ys,trend_coeff,exit_flag,info,Model,DynareOptions,BayesInfo,DynareResu
|
|||
% 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) stephane DOT adjemian AT univ DASH lemans DOT fr
|
||||
% frederic DOT karame AT univ DASH lemans DOT fr
|
||||
persistent init_flag restrict_variables_idx state_variables_idx mf0 mf1 number_of_state_variables
|
||||
|
||||
%global objective_function_penalty_base
|
||||
% Declaration of the penalty as a persistent variable.
|
||||
persistent init_flag
|
||||
persistent restrict_variables_idx observed_variables_idx state_variables_idx mf0 mf1
|
||||
persistent sample_size number_of_state_variables number_of_observed_variables number_of_structural_innovations
|
||||
info = 0;
|
||||
|
||||
% Initialization of the returned arguments.
|
||||
fval = [];
|
||||
ys = [];
|
||||
trend_coeff = [];
|
||||
exit_flag = 1;
|
||||
|
||||
% Set the number of observed variables
|
||||
%nvobs = DynareDataset.info.nvobs;
|
||||
nvobs = size(DynareDataset.data,1) ;
|
||||
|
||||
%------------------------------------------------------------------------------
|
||||
%----------------------------------------------------
|
||||
% 1. Get the structural parameters & define penalties
|
||||
%------------------------------------------------------------------------------
|
||||
%----------------------------------------------------
|
||||
|
||||
% Return, with endogenous penalty, if some parameters are smaller than the lower bound of the prior domain.
|
||||
%if (DynareOptions.mode_compute~=1) && any(xparam1<BayesInfo.lb)
|
||||
% k = find(xparam1(:) < BayesInfo.lb);
|
||||
% fval = objective_function_penalty_base+sum((BayesInfo.lb(k)-xparam1(k)).^2);
|
||||
% exit_flag = 0;
|
||||
% info = 41;
|
||||
% return
|
||||
%end
|
||||
% Test if some parameters are smaller than the lower bound of the prior domain.
|
||||
if any(xparam1<bounds.lb)
|
||||
info = 41;
|
||||
return
|
||||
end
|
||||
|
||||
% Return, with endogenous penalty, if some parameters are greater than the upper bound of the prior domain.
|
||||
%if (DynareOptions.mode_compute~=1) && any(xparam1>BayesInfo.ub)
|
||||
% k = find(xparam1(:)>BayesInfo.ub);
|
||||
% fval = objective_function_penalty_base+sum((xparam1(k)-BayesInfo.ub(k)).^2);
|
||||
% exit_flag = 0;
|
||||
% info = 42;
|
||||
% return
|
||||
%end
|
||||
% Test if some parameters are greater than the upper bound of the prior domain.
|
||||
if any(xparam1>bounds.ub)
|
||||
info = 42;
|
||||
return
|
||||
end
|
||||
|
||||
% Get the diagonal elements of the covariance matrices for the structural innovations (Q) and the measurement error (H).
|
||||
Q = Model.Sigma_e;
|
||||
|
|
@ -173,7 +71,7 @@ if EstimatedParameters.nvn
|
|||
end
|
||||
offset = offset+EstimatedParameters.nvn;
|
||||
else
|
||||
H = zeros(nvobs);
|
||||
H = zeros(size(DynareDataset.data, 1));
|
||||
end
|
||||
|
||||
% Get the off-diagonal elements of the covariance matrix for the structural innovations. Test if Q is positive definite.
|
||||
|
|
@ -185,18 +83,12 @@ if EstimatedParameters.ncx
|
|||
Q(k2,k1) = Q(k1,k2);
|
||||
end
|
||||
% Try to compute the cholesky decomposition of Q (possible iff Q is positive definite)
|
||||
% [CholQ,testQ] = chol(Q);
|
||||
% if testQ
|
||||
% The variance-covariance matrix of the structural innovations is not definite positive. We have to compute the eigenvalues of this matrix in order to build the endogenous penalty.
|
||||
% a = diag(eig(Q));
|
||||
% k = find(a < 0);
|
||||
% if k > 0
|
||||
% fval = objective_function_penalty_base+sum(-a(k));
|
||||
% exit_flag = 0;
|
||||
% info = 43;
|
||||
% return
|
||||
% end
|
||||
% end
|
||||
[~, testQ] = chol(Q);
|
||||
if testQ
|
||||
% The variance-covariance matrix of the structural innovations is not definite positive.
|
||||
info = 43;
|
||||
return
|
||||
end
|
||||
offset = offset+EstimatedParameters.ncx;
|
||||
end
|
||||
|
||||
|
|
@ -210,18 +102,12 @@ if EstimatedParameters.ncn
|
|||
H(k2,k1) = H(k1,k2);
|
||||
end
|
||||
% Try to compute the cholesky decomposition of H (possible iff H is positive definite)
|
||||
% [CholH,testH] = chol(H);
|
||||
% if testH
|
||||
% The variance-covariance matrix of the measurement errors is not definite positive. We have to compute the eigenvalues of this matrix in order to build the endogenous penalty.
|
||||
% a = diag(eig(H));
|
||||
% k = find(a < 0);
|
||||
% if k > 0
|
||||
% fval = objective_function_penalty_base+sum(-a(k));
|
||||
% exit_flag = 0;
|
||||
% info = 44;
|
||||
% return
|
||||
% end
|
||||
% end
|
||||
[~, testH] = chol(H);
|
||||
if testH
|
||||
% The variance-covariance matrix of the measurement errors is not definite positive.
|
||||
info = 44;
|
||||
return
|
||||
end
|
||||
offset = offset+EstimatedParameters.ncn;
|
||||
end
|
||||
|
||||
|
|
@ -238,55 +124,18 @@ Model.H = H;
|
|||
% 2. call model setup & reduction program
|
||||
%------------------------------------------------------------------------------
|
||||
|
||||
% Linearize the model around the deterministic sdteadystate and extract the matrices of the state equation (T and R).
|
||||
[T,R,SteadyState,info,Model,DynareOptions,DynareResults] = dynare_resolve(Model,DynareOptions,DynareResults,'restrict');
|
||||
warning('off', 'MATLAB:nearlySingularMatrix')
|
||||
[~, ~, ~, info, Model, DynareOptions, DynareResults] = ...
|
||||
dynare_resolve(Model, DynareOptions, DynareResults, 'restrict');
|
||||
warning('on', 'MATLAB:nearlySingularMatrix')
|
||||
|
||||
%disp(info)
|
||||
|
||||
if info(1) ~= 0
|
||||
ReducedForm = 0 ;
|
||||
exit_flag = 55;
|
||||
if info(1)~=0
|
||||
if nargout==5
|
||||
ReducedForm = 0;
|
||||
end
|
||||
return
|
||||
end
|
||||
|
||||
% Define a vector of indices for the observed variables. Is this really usefull?...
|
||||
BayesInfo.mf = BayesInfo.mf1;
|
||||
|
||||
% Define the deterministic linear trend of the measurement equation.
|
||||
if DynareOptions.noconstant
|
||||
constant = zeros(nvobs,1);
|
||||
else
|
||||
if DynareOptions.loglinear
|
||||
constant = log(SteadyState(BayesInfo.mfys));
|
||||
else
|
||||
constant = SteadyState(BayesInfo.mfys);
|
||||
end
|
||||
end
|
||||
|
||||
% Define the deterministic linear trend of the measurement equation.
|
||||
%if BayesInfo.with_trend
|
||||
% trend_coeff = zeros(DynareDataset.info.nvobs,1);
|
||||
% t = DynareOptions.trend_coeffs;
|
||||
% for i=1:length(t)
|
||||
% if ~isempty(t{i})
|
||||
% trend_coeff(i) = evalin('base',t{i});
|
||||
% end
|
||||
% end
|
||||
% trend = repmat(constant,1,DynareDataset.info.ntobs)+trend_coeff*[1:DynareDataset.info.ntobs];
|
||||
%else
|
||||
% trend = repmat(constant,1,DynareDataset.info.ntobs);
|
||||
%end
|
||||
|
||||
% Get needed informations for kalman filter routines.
|
||||
start = DynareOptions.presample+1;
|
||||
np = size(T,1);
|
||||
mf = BayesInfo.mf;
|
||||
Y = transpose(DynareDataset.data);
|
||||
|
||||
%------------------------------------------------------------------------------
|
||||
% 3. Initial condition of the Kalman filter
|
||||
%------------------------------------------------------------------------------
|
||||
|
||||
% Get decision rules and transition equations.
|
||||
dr = DynareResults.dr;
|
||||
|
||||
|
|
@ -295,37 +144,37 @@ if isempty(init_flag)
|
|||
mf0 = BayesInfo.mf0;
|
||||
mf1 = BayesInfo.mf1;
|
||||
restrict_variables_idx = dr.restrict_var_list;
|
||||
observed_variables_idx = restrict_variables_idx(mf1);
|
||||
state_variables_idx = restrict_variables_idx(mf0);
|
||||
sample_size = size(Y,2);
|
||||
state_variables_idx = restrict_variables_idx(mf0);
|
||||
number_of_state_variables = length(mf0);
|
||||
number_of_observed_variables = length(mf1);
|
||||
number_of_structural_innovations = length(Q);
|
||||
init_flag = 1;
|
||||
init_flag = true;
|
||||
end
|
||||
|
||||
ReducedForm.ghx = dr.ghx(restrict_variables_idx,:);
|
||||
ReducedForm.ghu = dr.ghu(restrict_variables_idx,:);
|
||||
ReducedForm.steadystate = dr.ys(dr.order_var(restrict_variables_idx));
|
||||
if DynareOptions.order>1
|
||||
ReducedForm.ghxx = dr.ghxx(restrict_variables_idx,:);
|
||||
ReducedForm.ghuu = dr.ghuu(restrict_variables_idx,:);
|
||||
ReducedForm.ghxu = dr.ghxu(restrict_variables_idx,:);
|
||||
ReducedForm.constant = ReducedForm.steadystate + .5*dr.ghs2(restrict_variables_idx);
|
||||
else
|
||||
ReducedForm.ghxx = zeros(size(restrict_variables_idx,1),size(dr.kstate,2));
|
||||
ReducedForm.ghuu = zeros(size(restrict_variables_idx,1),size(dr.ghu,2));
|
||||
ReducedForm.ghxu = zeros(size(restrict_variables_idx,1),size(dr.ghx,2));
|
||||
ReducedForm.constant = ReducedForm.steadystate ;
|
||||
end
|
||||
ReducedForm.state_variables_steady_state = dr.ys(dr.order_var(state_variables_idx));
|
||||
ReducedForm.Q = Q;
|
||||
ReducedForm.H = H;
|
||||
ReducedForm.mf0 = mf0;
|
||||
ReducedForm.mf1 = mf1;
|
||||
|
||||
% Set initial condition for t=1
|
||||
if observation_number==1
|
||||
% Return reduced form model.
|
||||
if nargout>4
|
||||
ReducedForm.ghx = dr.ghx(restrict_variables_idx,:);
|
||||
ReducedForm.ghu = dr.ghu(restrict_variables_idx,:);
|
||||
ReducedForm.steadystate = dr.ys(dr.order_var(restrict_variables_idx));
|
||||
if DynareOptions.order>1
|
||||
ReducedForm.ghxx = dr.ghxx(restrict_variables_idx,:);
|
||||
ReducedForm.ghuu = dr.ghuu(restrict_variables_idx,:);
|
||||
ReducedForm.ghxu = dr.ghxu(restrict_variables_idx,:);
|
||||
ReducedForm.constant = ReducedForm.steadystate + .5*dr.ghs2(restrict_variables_idx);
|
||||
else
|
||||
ReducedForm.ghxx = zeros(size(restrict_variables_idx,1),size(dr.kstate,2));
|
||||
ReducedForm.ghuu = zeros(size(restrict_variables_idx,1),size(dr.ghu,2));
|
||||
ReducedForm.ghxu = zeros(size(restrict_variables_idx,1),size(dr.ghx,2));
|
||||
ReducedForm.constant = ReducedForm.steadystate ;
|
||||
end
|
||||
ReducedForm.state_variables_steady_state = dr.ys(dr.order_var(state_variables_idx));
|
||||
ReducedForm.Q = Q;
|
||||
ReducedForm.H = H;
|
||||
ReducedForm.mf0 = mf0;
|
||||
ReducedForm.mf1 = mf1;
|
||||
end
|
||||
|
||||
% Set initial condition
|
||||
if setinitialcondition
|
||||
switch DynareOptions.particle.initialization
|
||||
case 1% Initial state vector covariance is the ergodic variance associated to the first order Taylor-approximation of the model.
|
||||
StateVectorMean = ReducedForm.constant(mf0);
|
||||
|
|
@ -347,4 +196,4 @@ if observation_number==1
|
|||
end
|
||||
ReducedForm.StateVectorMean = StateVectorMean;
|
||||
ReducedForm.StateVectorVariance = StateVectorVariance;
|
||||
end
|
||||
end
|
||||
Loading…
Reference in New Issue