Replaced particle folder by a Git submodule (particles). Adapted path in dynare_config.
Stéphane Adjemian (Telemachus)
parent
7b90fd9c32
commit
e143f8ef2e
|
|
@ -13,3 +13,6 @@
|
|||
[submodule "matlab/utilities/tests"]
|
||||
path = matlab/utilities/tests
|
||||
url = https://github.com/DynareTeam/m-unit-tests.git
|
||||
[submodule "matlab/particles"]
|
||||
path = matlab/particles
|
||||
url = https://github.com/DynareTeam/particles.git
|
||||
|
|
|
|||
|
|
@ -44,7 +44,6 @@ if ~nargin || nargin==1
|
|||
verbose = 1;
|
||||
end
|
||||
|
||||
|
||||
addpath([dynareroot '/distributions/'])
|
||||
addpath([dynareroot '/kalman/'])
|
||||
addpath([dynareroot '/kalman/likelihood'])
|
||||
|
|
@ -54,7 +53,7 @@ addpath([dynareroot '/ms-sbvar/'])
|
|||
addpath([dynareroot '/ms-sbvar/identification/'])
|
||||
addpath([dynareroot '../contrib/ms-sbvar/TZcode/MatlabFiles/'])
|
||||
addpath([dynareroot '/parallel/'])
|
||||
addpath([dynareroot '/particle/'])
|
||||
addpath([dynareroot '/particles/src'])
|
||||
addpath([dynareroot '/gsa/'])
|
||||
addpath([dynareroot '/ep/'])
|
||||
addpath([dynareroot '/lmmcp/'])
|
||||
|
|
|
|||
|
|
@ -1,116 +0,0 @@
|
|||
function initial_distribution = auxiliary_initialization(ReducedForm,Y,start,DynareOptions)
|
||||
% Evaluates the likelihood of a nonlinear model with a particle filter allowing eventually resampling.
|
||||
%
|
||||
% INPUTS
|
||||
% ReducedForm [structure] Matlab's structure describing the reduced form model.
|
||||
% ReducedForm.measurement.H [double] (pp x pp) variance matrix of measurement errors.
|
||||
% ReducedForm.state.Q [double] (qq x qq) variance matrix of state errors.
|
||||
% ReducedForm.state.dr [structure] output of resol.m.
|
||||
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
|
||||
% start [integer] scalar, likelihood evaluation starts at 'start'.
|
||||
% mf [integer] pp*1 vector of indices.
|
||||
% number_of_particles [integer] scalar.
|
||||
%
|
||||
% OUTPUTS
|
||||
% LIK [double] scalar, likelihood
|
||||
% lik [double] vector, density of observations in each period.
|
||||
%
|
||||
% REFERENCES
|
||||
%
|
||||
% NOTES
|
||||
% The vector "lik" is used to evaluate the jacobian of the likelihood.
|
||||
|
||||
% Copyright (C) 2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
persistent init_flag mf0 mf1 number_of_particles
|
||||
persistent number_of_observed_variables number_of_structural_innovations
|
||||
|
||||
% Set default
|
||||
if isempty(start)
|
||||
start = 1;
|
||||
end
|
||||
|
||||
% Set flag for prunning
|
||||
%pruning = DynareOptions.particle.pruning;
|
||||
|
||||
% Get steady state and mean.
|
||||
%steadystate = ReducedForm.steadystate;
|
||||
constant = ReducedForm.constant;
|
||||
state_variables_steady_state = ReducedForm.state_variables_steady_state;
|
||||
|
||||
% Set persistent variables.
|
||||
if isempty(init_flag)
|
||||
mf0 = ReducedForm.mf0;
|
||||
mf1 = ReducedForm.mf1;
|
||||
number_of_observed_variables = length(mf1);
|
||||
number_of_structural_innovations = length(ReducedForm.Q);
|
||||
number_of_particles = DynareOptions.particle.number_of_particles;
|
||||
init_flag = 1;
|
||||
end
|
||||
|
||||
% Set local state space model (first order approximation).
|
||||
ghx = ReducedForm.ghx;
|
||||
ghu = ReducedForm.ghu;
|
||||
% Set local state space model (second order approximation).
|
||||
ghxx = ReducedForm.ghxx;
|
||||
ghuu = ReducedForm.ghuu;
|
||||
ghxu = ReducedForm.ghxu;
|
||||
|
||||
% Get covariance matrices
|
||||
Q = ReducedForm.Q;
|
||||
H = ReducedForm.H;
|
||||
if isempty(H)
|
||||
H = 0;
|
||||
end
|
||||
|
||||
% Get initial condition for the state vector.
|
||||
StateVectorMean = ReducedForm.StateVectorMean;
|
||||
StateVectorVarianceSquareRoot = reduced_rank_cholesky(ReducedForm.StateVectorVariance)';
|
||||
state_variance_rank = size(StateVectorVarianceSquareRoot,2);
|
||||
%Q_lower_triangular_cholesky = chol(Q)';
|
||||
%if pruning
|
||||
% StateVectorMean_ = StateVectorMean;
|
||||
% StateVectorVarianceSquareRoot_ = StateVectorVarianceSquareRoot;
|
||||
%end
|
||||
|
||||
% Set seed for randn().
|
||||
set_dynare_seed('default');
|
||||
|
||||
% Initialization of the likelihood.
|
||||
const_lik = log(2*pi)*number_of_observed_variables;
|
||||
|
||||
% Initialization of the weights across particles.
|
||||
weights = ones(1,number_of_particles)/number_of_particles ;
|
||||
StateVectors = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean);
|
||||
%if pruning
|
||||
% StateVectors_ = StateVectors;
|
||||
%end
|
||||
yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
|
||||
%if pruning
|
||||
% yhat_ = bsxfun(@minus,StateVectors_,state_variables_steady_state);
|
||||
% [tmp, tmp_] = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,number_of_particles),ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,DynareOptions.threads.local_state_space_iteration_2);
|
||||
%else
|
||||
tmp = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,number_of_particles),ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
|
||||
%end
|
||||
PredictedObservedMean = weights*(tmp(mf1,:)');
|
||||
PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:));
|
||||
dPredictedObservedMean = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean');
|
||||
PredictedObservedVariance = bsxfun(@times,weights,dPredictedObservedMean)*dPredictedObservedMean' + H;
|
||||
wtilde = exp(-.5*(const_lik+log(det(PredictedObservedVariance))+sum(PredictionError.*(PredictedObservedVariance\PredictionError),1))) ;
|
||||
tau_tilde = weights.*wtilde ;
|
||||
tau_tilde = tau_tilde/sum(tau_tilde);
|
||||
initial_distribution = resample(StateVectors',tau_tilde',DynareOptions)' ;
|
||||
|
|
@ -1,159 +0,0 @@
|
|||
function [LIK,lik] = auxiliary_particle_filter(ReducedForm,Y,start,DynareOptions)
|
||||
% Evaluates the likelihood of a nonlinear model with a particle filter allowing eventually resampling.
|
||||
%
|
||||
% INPUTS
|
||||
% ReducedForm [structure] Matlab's structure describing the reduced form model.
|
||||
% ReducedForm.measurement.H [double] (pp x pp) variance matrix of measurement errors.
|
||||
% ReducedForm.state.Q [double] (qq x qq) variance matrix of state errors.
|
||||
% ReducedForm.state.dr [structure] output of resol.m.
|
||||
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
|
||||
% start [integer] scalar, likelihood evaluation starts at 'start'.
|
||||
% mf [integer] pp*1 vector of indices.
|
||||
% number_of_particles [integer] scalar.
|
||||
%
|
||||
% OUTPUTS
|
||||
% LIK [double] scalar, likelihood
|
||||
% lik [double] vector, density of observations in each period.
|
||||
%
|
||||
% REFERENCES
|
||||
%
|
||||
% NOTES
|
||||
% The vector "lik" is used to evaluate the jacobian of the likelihood.
|
||||
|
||||
% Copyright (C) 2011-2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
persistent init_flag mf0 mf1 number_of_particles
|
||||
persistent sample_size number_of_state_variables number_of_observed_variables number_of_structural_innovations
|
||||
|
||||
% Set default
|
||||
if isempty(start)
|
||||
start = 1;
|
||||
end
|
||||
|
||||
% Set flag for prunning
|
||||
pruning = DynareOptions.particle.pruning;
|
||||
|
||||
% Get steady state and mean.
|
||||
steadystate = ReducedForm.steadystate;
|
||||
constant = ReducedForm.constant;
|
||||
state_variables_steady_state = ReducedForm.state_variables_steady_state;
|
||||
|
||||
% Set persistent variables.
|
||||
if isempty(init_flag)
|
||||
mf0 = ReducedForm.mf0;
|
||||
mf1 = ReducedForm.mf1;
|
||||
sample_size = size(Y,2);
|
||||
number_of_state_variables = length(mf0);
|
||||
number_of_observed_variables = length(mf1);
|
||||
number_of_structural_innovations = length(ReducedForm.Q);
|
||||
number_of_particles = DynareOptions.particle.number_of_particles;
|
||||
init_flag = 1;
|
||||
end
|
||||
|
||||
% Set local state space model (first order approximation).
|
||||
ghx = ReducedForm.ghx;
|
||||
ghu = ReducedForm.ghu;
|
||||
% Set local state space model (second order approximation).
|
||||
ghxx = ReducedForm.ghxx;
|
||||
ghuu = ReducedForm.ghuu;
|
||||
ghxu = ReducedForm.ghxu;
|
||||
|
||||
% Get covariance matrices
|
||||
Q = ReducedForm.Q;
|
||||
H = ReducedForm.H;
|
||||
if isempty(H)
|
||||
H = 0;
|
||||
end
|
||||
|
||||
% Get initial condition for the state vector.
|
||||
StateVectorMean = ReducedForm.StateVectorMean;
|
||||
StateVectorVarianceSquareRoot = reduced_rank_cholesky(ReducedForm.StateVectorVariance)';
|
||||
state_variance_rank = size(StateVectorVarianceSquareRoot,2);
|
||||
Q_lower_triangular_cholesky = chol(Q)';
|
||||
if pruning
|
||||
StateVectorMean_ = StateVectorMean;
|
||||
StateVectorVarianceSquareRoot_ = StateVectorVarianceSquareRoot;
|
||||
end
|
||||
|
||||
% Set seed for randn().
|
||||
set_dynare_seed('default');
|
||||
|
||||
% Initialization of the likelihood.
|
||||
const_lik = log(2*pi)*number_of_observed_variables;
|
||||
lik = NaN(sample_size,1);
|
||||
LIK = NaN;
|
||||
|
||||
% Initialization of the weights across particles.
|
||||
weights = ones(1,number_of_particles)/number_of_particles ;
|
||||
StateVectors = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean);
|
||||
if pruning
|
||||
StateVectors_ = StateVectors;
|
||||
end
|
||||
for t=1:sample_size
|
||||
yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
|
||||
if pruning
|
||||
yhat_ = bsxfun(@minus,StateVectors_,state_variables_steady_state);
|
||||
[tmp, tmp_] = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,number_of_particles),ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,DynareOptions.threads.local_state_space_iteration_2);
|
||||
else
|
||||
tmp = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,number_of_particles),ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
|
||||
end
|
||||
PredictedObservedMean = weights*(tmp(mf1,:)');
|
||||
PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:));
|
||||
dPredictedObservedMean = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean');
|
||||
PredictedObservedVariance = bsxfun(@times,weights,dPredictedObservedMean)*dPredictedObservedMean' +H;
|
||||
wtilde = exp(-.5*(const_lik+log(det(PredictedObservedVariance))+sum(PredictionError.*(PredictedObservedVariance\PredictionError),1))) ;
|
||||
tau_tilde = weights.*wtilde ;
|
||||
sum_tau_tilde = sum(tau_tilde) ;
|
||||
%var_wtilde = wtilde-sum_tau_tilde ;
|
||||
%var_wtilde = var_wtilde'*var_wtilde/(number_of_particles-1) ;
|
||||
lik(t) = log(sum_tau_tilde) ; %+ .5*var_wtilde/(number_of_particles*(sum_tau_tilde*sum_tau_tilde)) ;
|
||||
tau_tilde = tau_tilde/sum_tau_tilde;
|
||||
if pruning
|
||||
temp = resample([yhat' yhat_'],tau_tilde',DynareOptions);
|
||||
yhat = temp(:,1:number_of_state_variables)' ;
|
||||
yhat_ = temp(:,number_of_state_variables+1:2*number_of_state_variables)' ;
|
||||
else
|
||||
yhat = resample(yhat',tau_tilde',DynareOptions)' ;
|
||||
end
|
||||
if pruning
|
||||
[tmp, tmp_] = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,number_of_particles),ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,DynareOptions.threads.local_state_space_iteration_2);
|
||||
else
|
||||
tmp = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,number_of_particles),ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
|
||||
end
|
||||
PredictedObservedMean = weights*(tmp(mf1,:)');
|
||||
PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:));
|
||||
dPredictedObservedMean = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean');
|
||||
PredictedObservedVariance = bsxfun(@times,weights,dPredictedObservedMean)*dPredictedObservedMean' +H;
|
||||
wtilde = exp(-.5*(const_lik+log(det(PredictedObservedVariance))+sum(PredictionError.*(PredictedObservedVariance\PredictionError),1))) ;
|
||||
epsilon = Q_lower_triangular_cholesky*randn(number_of_structural_innovations,number_of_particles);
|
||||
if pruning
|
||||
[tmp, tmp_] = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,DynareOptions.threads.local_state_space_iteration_2);
|
||||
StateVectors_ = tmp_(mf0,:);
|
||||
else
|
||||
tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
|
||||
end
|
||||
StateVectors = tmp(mf0,:);
|
||||
PredictedObservedMean = mean(tmp(mf1,:),2);
|
||||
PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:));
|
||||
dPredictedObservedMean = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean);
|
||||
PredictedObservedVariance = (dPredictedObservedMean*dPredictedObservedMean')/number_of_particles + H;
|
||||
lnw = exp(-.5*(const_lik+log(det(PredictedObservedVariance))+sum(PredictionError.*(PredictedObservedVariance\PredictionError),1)));
|
||||
wtilde = lnw./wtilde;
|
||||
weights = wtilde/sum(wtilde);
|
||||
end
|
||||
|
||||
LIK = -sum(lik(start:end));
|
||||
|
|
@ -1,123 +0,0 @@
|
|||
function [ProposalStateVector,Weights] = conditional_filter_proposal(ReducedForm,obs,StateVectors,SampleWeights,Q_lower_triangular_cholesky,H_lower_triangular_cholesky,H,DynareOptions,normconst2)
|
||||
%
|
||||
% Computes the proposal for each past particle using Gaussian approximations
|
||||
% for the state errors and the Kalman filter
|
||||
%
|
||||
% INPUTS
|
||||
% reduced_form_model [structure] Matlab's structure describing the reduced form model.
|
||||
% reduced_form_model.measurement.H [double] (pp x pp) variance matrix of measurement errors.
|
||||
% reduced_form_model.state.Q [double] (qq x qq) variance matrix of state errors.
|
||||
% reduced_form_model.state.dr [structure] output of resol.m.
|
||||
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
|
||||
%
|
||||
% OUTPUTS
|
||||
% LIK [double] scalar, likelihood
|
||||
% lik [double] vector, density of observations in each period.
|
||||
%
|
||||
% REFERENCES
|
||||
%
|
||||
% NOTES
|
||||
% The vector "lik" is used to evaluate the jacobian of the likelihood.
|
||||
% Copyright (C) 2012-2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
%
|
||||
% AUTHOR(S) frederic DOT karame AT univ DASH lemans DOT fr
|
||||
% stephane DOT adjemian AT univ DASH lemans DOT fr
|
||||
|
||||
persistent init_flag2 mf0 mf1
|
||||
persistent number_of_state_variables number_of_observed_variables
|
||||
persistent number_of_structural_innovations
|
||||
|
||||
% Set local state space model (first-order approximation).
|
||||
ghx = ReducedForm.ghx;
|
||||
ghu = ReducedForm.ghu;
|
||||
% Set local state space model (second-order approximation).
|
||||
ghxx = ReducedForm.ghxx;
|
||||
ghuu = ReducedForm.ghuu;
|
||||
ghxu = ReducedForm.ghxu;
|
||||
|
||||
if any(any(isnan(ghx))) || any(any(isnan(ghu))) || any(any(isnan(ghxx))) || any(any(isnan(ghuu))) || any(any(isnan(ghxu))) || ...
|
||||
any(any(isinf(ghx))) || any(any(isinf(ghu))) || any(any(isinf(ghxx))) || any(any(isinf(ghuu))) || any(any(isinf(ghxu))) ...
|
||||
any(any(abs(ghx)>1e4)) || any(any(abs(ghu)>1e4)) || any(any(abs(ghxx)>1e4)) || any(any(abs(ghuu)>1e4)) || any(any(abs(ghxu)>1e4))
|
||||
ghx
|
||||
ghu
|
||||
ghxx
|
||||
ghuu
|
||||
ghxu
|
||||
end
|
||||
|
||||
constant = ReducedForm.constant;
|
||||
state_variables_steady_state = ReducedForm.state_variables_steady_state;
|
||||
|
||||
% Set persistent variables.
|
||||
if isempty(init_flag2)
|
||||
mf0 = ReducedForm.mf0;
|
||||
mf1 = ReducedForm.mf1;
|
||||
number_of_state_variables = length(mf0);
|
||||
number_of_observed_variables = length(mf1);
|
||||
number_of_structural_innovations = length(ReducedForm.Q);
|
||||
init_flag2 = 1;
|
||||
end
|
||||
|
||||
if DynareOptions.particle.proposal_approximation.cubature || DynareOptions.particle.proposal_approximation.montecarlo
|
||||
[nodes,weights] = spherical_radial_sigma_points(number_of_structural_innovations);
|
||||
weights_c = weights ;
|
||||
elseif DynareOptions.particle.proposal_approximation.unscented
|
||||
[nodes,weights,weights_c] = unscented_sigma_points(number_of_structural_innovations,DynareOptions);
|
||||
else
|
||||
error('Estimation: This approximation for the proposal is not implemented or unknown!')
|
||||
end
|
||||
|
||||
epsilon = Q_lower_triangular_cholesky*(nodes') ;
|
||||
yhat = repmat(StateVectors-state_variables_steady_state,1,size(epsilon,2)) ;
|
||||
|
||||
tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
|
||||
|
||||
PredictedStateMean = tmp(mf0,:)*weights ;
|
||||
PredictedObservedMean = tmp(mf1,:)*weights;
|
||||
|
||||
if DynareOptions.particle.proposal_approximation.cubature || DynareOptions.particle.proposal_approximation.montecarlo
|
||||
PredictedStateMean = sum(PredictedStateMean,2) ;
|
||||
PredictedObservedMean = sum(PredictedObservedMean,2) ;
|
||||
dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean)'.*sqrt(weights) ;
|
||||
dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean)'.*sqrt(weights);
|
||||
big_mat = [dObserved dState; [H_lower_triangular_cholesky zeros(number_of_observed_variables,number_of_state_variables)] ];
|
||||
[mat1,mat] = qr2(big_mat,0);
|
||||
mat = mat';
|
||||
clear('mat1');
|
||||
PredictedObservedVarianceSquareRoot = mat(1:number_of_observed_variables,1:number_of_observed_variables);
|
||||
CovarianceObservedStateSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),1:number_of_observed_variables);
|
||||
StateVectorVarianceSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),number_of_observed_variables+(1:number_of_state_variables));
|
||||
StateVectorMean = PredictedStateMean + (CovarianceObservedStateSquareRoot/PredictedObservedVarianceSquareRoot)*(obs - PredictedObservedMean);
|
||||
else
|
||||
dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean);
|
||||
dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean);
|
||||
PredictedStateVariance = dState*diag(weights_c)*dState';
|
||||
PredictedObservedVariance = dObserved*diag(weights_c)*dObserved' + H;
|
||||
PredictedStateAndObservedCovariance = dState*diag(weights_c)*dObserved';
|
||||
KalmanFilterGain = PredictedStateAndObservedCovariance/PredictedObservedVariance ;
|
||||
StateVectorMean = PredictedStateMean + KalmanFilterGain*(obs - PredictedObservedMean);
|
||||
StateVectorVariance = PredictedStateVariance - KalmanFilterGain*PredictedObservedVariance*KalmanFilterGain';
|
||||
StateVectorVariance = .5*(StateVectorVariance+StateVectorVariance');
|
||||
StateVectorVarianceSquareRoot = reduced_rank_cholesky(StateVectorVariance)';
|
||||
end
|
||||
|
||||
ProposalStateVector = StateVectorVarianceSquareRoot*randn(size(StateVectorVarianceSquareRoot,2),1)+StateVectorMean ;
|
||||
ypred = measurement_equations(ProposalStateVector,ReducedForm,DynareOptions) ;
|
||||
foo = H_lower_triangular_cholesky \ (obs - ypred) ;
|
||||
likelihood = exp(-0.5*(foo)'*foo)/normconst2 + 1e-99 ;
|
||||
Weights = SampleWeights.*likelihood;
|
||||
|
|
@ -1,125 +0,0 @@
|
|||
function [LIK,lik] = conditional_particle_filter(ReducedForm,Y,start,DynareOptions)
|
||||
%
|
||||
% Evaluates the likelihood of a non-linear model with a particle filter
|
||||
% - the proposal is built using the Kalman updating step for each particle.
|
||||
% - we need draws in the errors distributions
|
||||
% Whether we use Monte-Carlo draws from a multivariate gaussian distribution
|
||||
% as in Amisano & Tristani (JEDC 2010).
|
||||
% Whether we use multidimensional Gaussian sparse grids approximations:
|
||||
% - a univariate Kronrod-Paterson Gaussian quadrature combined by the Smolyak
|
||||
% operator (ref: Winschel & Kratzig, 2010).
|
||||
% - a spherical-radial cubature (ref: Arasaratnam & Haykin, 2009a,2009b).
|
||||
% - a scaled unscented transform cubature (ref: Julier & Uhlmann 1997, van der
|
||||
% Merwe & Wan 2003).
|
||||
%
|
||||
% Pros:
|
||||
% - Allows using current observable information in the proposal
|
||||
% - The use of sparse grids Gaussian approximation is much faster than the Monte-Carlo approach
|
||||
% Cons:
|
||||
% - The use of the Kalman updating step may biais the proposal distribution since
|
||||
% it has been derived in a linear context and is implemented in a nonlinear
|
||||
% context. That is why particle resampling is performed.
|
||||
%
|
||||
% INPUTS
|
||||
% reduced_form_model [structure] Matlab's structure describing the reduced form model.
|
||||
% reduced_form_model.measurement.H [double] (pp x pp) variance matrix of measurement errors.
|
||||
% reduced_form_model.state.Q [double] (qq x qq) variance matrix of state errors.
|
||||
% reduced_form_model.state.dr [structure] output of resol.m.
|
||||
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
|
||||
% start [integer] scalar, likelihood evaluation starts at 'start'.
|
||||
% smolyak_accuracy [integer] scalar.
|
||||
%
|
||||
% OUTPUTS
|
||||
% LIK [double] scalar, likelihood
|
||||
% lik [double] vector, density of observations in each period.
|
||||
%
|
||||
% REFERENCES
|
||||
%
|
||||
% NOTES
|
||||
% The vector "lik" is used to evaluate the jacobian of the likelihood.
|
||||
% Copyright (C) 2009-2010 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
% AUTHOR(S) frederic DOT karame AT univ DASH lemans DOT fr
|
||||
% stephane DOT adjemian AT univ DASH lemans DOT fr
|
||||
|
||||
persistent init_flag mf0 mf1
|
||||
persistent number_of_particles
|
||||
persistent sample_size number_of_state_variables number_of_observed_variables
|
||||
|
||||
% Set default
|
||||
if isempty(start)
|
||||
start = 1;
|
||||
end
|
||||
|
||||
% Set persistent variables.
|
||||
if isempty(init_flag)
|
||||
mf0 = ReducedForm.mf0;
|
||||
mf1 = ReducedForm.mf1;
|
||||
sample_size = size(Y,2);
|
||||
number_of_state_variables = length(mf0);
|
||||
number_of_observed_variables = length(mf1);
|
||||
init_flag = 1;
|
||||
number_of_particles = DynareOptions.particle.number_of_particles ;
|
||||
end
|
||||
|
||||
% Get covariance matrices
|
||||
Q = ReducedForm.Q;
|
||||
H = ReducedForm.H;
|
||||
if isempty(H)
|
||||
H = 0;
|
||||
H_lower_triangular_cholesky = 0;
|
||||
else
|
||||
H_lower_triangular_cholesky = reduced_rank_cholesky(H)';
|
||||
end
|
||||
|
||||
% Get initial condition for the state vector.
|
||||
StateVectorMean = ReducedForm.StateVectorMean;
|
||||
StateVectorVarianceSquareRoot = reduced_rank_cholesky(ReducedForm.StateVectorVariance)';
|
||||
state_variance_rank = size(StateVectorVarianceSquareRoot,2);
|
||||
Q_lower_triangular_cholesky = reduced_rank_cholesky(Q)';
|
||||
|
||||
% Set seed for randn().
|
||||
set_dynare_seed('default');
|
||||
|
||||
% Initialization of the likelihood.
|
||||
normconst2 = log(2*pi)*number_of_observed_variables*prod(diag(H_lower_triangular_cholesky)) ;
|
||||
lik = NaN(sample_size,1);
|
||||
LIK = NaN;
|
||||
|
||||
ks = 0 ;
|
||||
|
||||
StateParticles = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean);
|
||||
SampleWeights = ones(1,number_of_particles)/number_of_particles ;
|
||||
for t=1:sample_size
|
||||
for i=1:number_of_particles
|
||||
[StateParticles(:,i),SampleWeights(i)] = ...
|
||||
conditional_filter_proposal(ReducedForm,Y(:,t),StateParticles(:,i),SampleWeights(i),Q_lower_triangular_cholesky,H_lower_triangular_cholesky,H,DynareOptions,normconst2) ;
|
||||
end
|
||||
SumSampleWeights = sum(SampleWeights) ;
|
||||
lik(t) = log(SumSampleWeights) ;
|
||||
SampleWeights = SampleWeights./SumSampleWeights ;
|
||||
if (DynareOptions.particle.resampling.status.generic && neff(SampleWeights)<DynareOptions.particle.resampling.threshold*sample_size) || DynareOptions.particle.resampling.status.systematic
|
||||
ks = ks + 1 ;
|
||||
StateParticles = resample(StateParticles',SampleWeights',DynareOptions)';
|
||||
SampleWeights = ones(1,number_of_particles)/number_of_particles ;
|
||||
end
|
||||
end
|
||||
|
||||
LIK = -sum(lik(start:end));
|
||||
|
||||
|
||||
|
|
@ -1,52 +0,0 @@
|
|||
function [StateMu,StateSqrtP,StateWeights] = fit_gaussian_mixture(X,StateMu,StateSqrtP,StateWeights,crit,niters,check)
|
||||
|
||||
% Copyright (C) 2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
[dim,Ndata] = size(X);
|
||||
M = size(StateMu,2) ;
|
||||
if check % Ensure that covariances don't collapse
|
||||
MIN_COVAR_SQRT = sqrt(eps);
|
||||
init_covars = StateSqrtP;
|
||||
end
|
||||
eold = -Inf;
|
||||
for n=1:niters
|
||||
% Calculate posteriors based on old parameters
|
||||
[prior,likelihood,marginal,posterior] = probability(StateMu,StateSqrtP,StateWeights,X);
|
||||
e = sum(log(marginal));
|
||||
if (n > 1 && abs((e - eold)/eold) < crit)
|
||||
return;
|
||||
else
|
||||
eold = e;
|
||||
end
|
||||
new_pr = (sum(posterior,2))';
|
||||
StateWeights = new_pr/Ndata;
|
||||
StateMu = bsxfun(@rdivide,(posterior*X')',new_pr);
|
||||
for j=1:M
|
||||
diffs = bsxfun(@minus,X,StateMu(:,j));
|
||||
tpost = (1/sqrt(new_pr(j)))*sqrt(posterior(j,:));
|
||||
diffs = bsxfun(@times,diffs,tpost);
|
||||
[foo,tcov] = qr2(diffs',0);
|
||||
StateSqrtP(:,:,j) = tcov';
|
||||
if check
|
||||
if min(abs(diag(StateSqrtP(:,:,j)))) < MIN_COVAR_SQRT
|
||||
StateSqrtP(:,:,j) = init_covars(:,:,j);
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
|
|
@ -1,52 +0,0 @@
|
|||
function IncrementalWeights = gaussian_densities(obs,mut_t,sqr_Pss_t_t,st_t_1,sqr_Pss_t_t_1,particles,H,normconst,weigths1,weigths2,ReducedForm,DynareOptions)
|
||||
%
|
||||
% Elements to calculate the importance sampling ratio
|
||||
%
|
||||
% INPUTS
|
||||
% reduced_form_model [structure] Matlab's structure describing the reduced form model.
|
||||
% reduced_form_model.measurement.H [double] (pp x pp) variance matrix of measurement errors.
|
||||
% reduced_form_model.state.Q [double] (qq x qq) variance matrix of state errors.
|
||||
% reduced_form_model.state.dr [structure] output of resol.m.
|
||||
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
|
||||
% start [integer] scalar, likelihood evaluation starts at 'start'.
|
||||
% smolyak_accuracy [integer] scalar.
|
||||
%
|
||||
% OUTPUTS
|
||||
% LIK [double] scalar, likelihood
|
||||
% lik [double] vector, density of observations in each period.
|
||||
%
|
||||
% REFERENCES
|
||||
%
|
||||
% NOTES
|
||||
% The vector "lik" is used to evaluate the jacobian of the likelihood.
|
||||
% Copyright (C) 2009-2010 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
% proposal density
|
||||
proposal = probability2(mut_t,sqr_Pss_t_t,particles) ;
|
||||
% prior density
|
||||
prior = probability2(st_t_1,sqr_Pss_t_t_1,particles) ;
|
||||
% likelihood
|
||||
yt_t_1_i = measurement_equations(particles,ReducedForm,DynareOptions) ;
|
||||
eta_t_i = bsxfun(@minus,obs,yt_t_1_i)' ;
|
||||
yt_t_1 = sum(yt_t_1_i*weigths1,2) ;
|
||||
tmp = bsxfun(@minus,yt_t_1_i,yt_t_1) ;
|
||||
Pyy = bsxfun(@times,weigths2',tmp)*tmp' + H ;
|
||||
sqr_det = sqrt(det(Pyy)) ;
|
||||
foo = (eta_t_i/Pyy).*eta_t_i ;
|
||||
likelihood = exp(-0.5*sum(foo,2))/(normconst*sqr_det) + 1e-99 ;
|
||||
IncrementalWeights = likelihood.*prior./proposal ;
|
||||
|
|
@ -1,162 +0,0 @@
|
|||
function [LIK,lik] = gaussian_filter(ReducedForm,Y,start,DynareOptions)
|
||||
% Evaluates the likelihood of a non-linear model approximating the
|
||||
% predictive (prior) and filtered (posterior) densities for state variables
|
||||
% by gaussian distributions.
|
||||
% Gaussian approximation is done by:
|
||||
% - a Kronrod-Paterson gaussian quadrature with a limited number of nodes.
|
||||
% Multidimensional quadrature is obtained by the Smolyak operator (ref: Winschel & Kratzig, 2010).
|
||||
% - a spherical-radial cubature (ref: Arasaratnam & Haykin, 2008,2009).
|
||||
% - a scaled unscented transform cubature (ref: )
|
||||
% - Monte-Carlo draws from a multivariate gaussian distribution.
|
||||
% First and second moments of prior and posterior state densities are computed
|
||||
% from the resulting nodes/particles and allows to generate new distributions at the
|
||||
% following observation.
|
||||
% => The use of nodes is much faster than Monte-Carlo Gaussian particle and standard particles
|
||||
% filters since it treats a lesser number of particles and there is no need
|
||||
% of resampling.
|
||||
% However, estimations may reveal biaised if the model is truly non-gaussian
|
||||
% since predictive and filtered densities are unimodal.
|
||||
%
|
||||
% INPUTS
|
||||
% reduced_form_model [structure] Matlab's structure describing the reduced form model.
|
||||
% reduced_form_model.measurement.H [double] (pp x pp) variance matrix of measurement errors.
|
||||
% reduced_form_model.state.Q [double] (qq x qq) variance matrix of state errors.
|
||||
% reduced_form_model.state.dr [structure] output of resol.m.
|
||||
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
|
||||
% start [integer] scalar, likelihood evaluation starts at 'start'.
|
||||
% smolyak_accuracy [integer] scalar.
|
||||
%
|
||||
% OUTPUTS
|
||||
% LIK [double] scalar, likelihood
|
||||
% lik [double] vector, density of observations in each period.
|
||||
%
|
||||
% REFERENCES
|
||||
%
|
||||
% NOTES
|
||||
% The vector "lik" is used to evaluate the jacobian of the likelihood.
|
||||
% Copyright (C) 2009-2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
persistent init_flag mf0 mf1
|
||||
persistent nodes2 weights2 weights_c2 number_of_particles
|
||||
persistent sample_size number_of_state_variables number_of_observed_variables
|
||||
|
||||
% Set default
|
||||
if isempty(start)
|
||||
start = 1;
|
||||
end
|
||||
|
||||
% Set persistent variables.
|
||||
if isempty(init_flag)
|
||||
mf0 = ReducedForm.mf0;
|
||||
mf1 = ReducedForm.mf1;
|
||||
sample_size = size(Y,2);
|
||||
number_of_state_variables = length(mf0);
|
||||
number_of_observed_variables = length(mf1);
|
||||
number_of_particles = DynareOptions.particle.number_of_particles;
|
||||
init_flag = 1;
|
||||
end
|
||||
|
||||
% compute gaussian quadrature nodes and weights on states and shocks
|
||||
if isempty(nodes2)
|
||||
if DynareOptions.particle.distribution_approximation.cubature
|
||||
[nodes2,weights2] = spherical_radial_sigma_points(number_of_state_variables);
|
||||
weights_c2 = weights2;
|
||||
elseif DynareOptions.particle.distribution_approximation.unscented
|
||||
[nodes2,weights2,weights_c2] = unscented_sigma_points(number_of_state_variables,DynareOptions);
|
||||
else
|
||||
if ~DynareOptions.particle.distribution_approximation.montecarlo
|
||||
error('Estimation: This approximation for the proposal is not implemented or unknown!')
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
if DynareOptions.particle.distribution_approximation.montecarlo
|
||||
set_dynare_seed('default');
|
||||
end
|
||||
|
||||
% Get covariance matrices
|
||||
Q = ReducedForm.Q;
|
||||
H = ReducedForm.H;
|
||||
if isempty(H)
|
||||
H = 0;
|
||||
H_lower_triangular_cholesky = 0;
|
||||
else
|
||||
H_lower_triangular_cholesky = reduced_rank_cholesky(H)';
|
||||
end
|
||||
|
||||
% Get initial condition for the state vector.
|
||||
StateVectorMean = ReducedForm.StateVectorMean;
|
||||
StateVectorVarianceSquareRoot = reduced_rank_cholesky(ReducedForm.StateVectorVariance)';
|
||||
state_variance_rank = size(StateVectorVarianceSquareRoot,2);
|
||||
Q_lower_triangular_cholesky = reduced_rank_cholesky(Q)';
|
||||
|
||||
% Initialization of the likelihood.
|
||||
const_lik = (2*pi)^(number_of_observed_variables/2) ;
|
||||
lik = NaN(sample_size,1);
|
||||
LIK = NaN;
|
||||
|
||||
SampleWeights = 1/number_of_particles ;
|
||||
ks = 0 ;
|
||||
%Estimate = zeros(number_of_state_variables,sample_size) ;
|
||||
%V_Estimate = zeros(number_of_state_variables,number_of_state_variables,sample_size) ;
|
||||
for t=1:sample_size
|
||||
% build the proposal
|
||||
[PredictedStateMean,PredictedStateVarianceSquareRoot,StateVectorMean,StateVectorVarianceSquareRoot] = ...
|
||||
gaussian_filter_bank(ReducedForm,Y(:,t),StateVectorMean,StateVectorVarianceSquareRoot,Q_lower_triangular_cholesky,H_lower_triangular_cholesky,H,DynareOptions) ;
|
||||
%Estimate(:,t) = PredictedStateMean ;
|
||||
%V_Estimate(:,:,t) = PredictedStateVarianceSquareRoot ;
|
||||
if DynareOptions.particle.distribution_approximation.cubature || DynareOptions.particle.distribution_approximation.unscented
|
||||
StateParticles = bsxfun(@plus,StateVectorMean,StateVectorVarianceSquareRoot*nodes2') ;
|
||||
IncrementalWeights = ...
|
||||
gaussian_densities(Y(:,t),StateVectorMean,...
|
||||
StateVectorVarianceSquareRoot,PredictedStateMean,...
|
||||
PredictedStateVarianceSquareRoot,StateParticles,H,const_lik,...
|
||||
weights2,weights_c2,ReducedForm,DynareOptions) ;
|
||||
SampleWeights = weights2.*IncrementalWeights ;
|
||||
SumSampleWeights = sum(SampleWeights) ;
|
||||
lik(t) = log(SumSampleWeights) ;
|
||||
SampleWeights = SampleWeights./SumSampleWeights ;
|
||||
else % Monte-Carlo draws
|
||||
StateParticles = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean) ;
|
||||
IncrementalWeights = ...
|
||||
gaussian_densities(Y(:,t),StateVectorMean,...
|
||||
StateVectorVarianceSquareRoot,PredictedStateMean,...
|
||||
PredictedStateVarianceSquareRoot,StateParticles,H,const_lik,...
|
||||
1/number_of_particles,1/number_of_particles,ReducedForm,DynareOptions) ;
|
||||
SampleWeights = SampleWeights.*IncrementalWeights ;
|
||||
SumSampleWeights = sum(SampleWeights) ;
|
||||
%VarSampleWeights = IncrementalWeights-SumSampleWeights ;
|
||||
%VarSampleWeights = VarSampleWeights*VarSampleWeights'/(number_of_particles-1) ;
|
||||
lik(t) = log(SumSampleWeights) ; %+ .5*VarSampleWeights/(number_of_particles*(SumSampleWeights*SumSampleWeights)) ;
|
||||
SampleWeights = SampleWeights./SumSampleWeights ;
|
||||
Neff = 1/sum(bsxfun(@power,SampleWeights,2)) ;
|
||||
if (Neff<.5*sample_size && DynareOptions.particle.resampling.status.generic) || DynareOptions.particle.resampling.status.systematic
|
||||
ks = ks + 1 ;
|
||||
StateParticles = resample(StateParticles',SampleWeights,DynareOptions)' ;
|
||||
StateVectorMean = mean(StateParticles,2) ;
|
||||
StateVectorVarianceSquareRoot = reduced_rank_cholesky( (StateParticles*StateParticles')/(number_of_particles-1) - StateVectorMean*(StateVectorMean') )';
|
||||
SampleWeights = 1/number_of_particles ;
|
||||
elseif DynareOptions.particle.resampling.status.none
|
||||
StateVectorMean = (sampleWeights*StateParticles)' ;
|
||||
temp = sqrt(SampleWeights').*StateParticles ;
|
||||
StateVectorVarianceSquareRoot = reduced_rank_cholesky( temp'*temp - StateVectorMean*(StateVectorMean') )';
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
LIK = -sum(lik(start:end));
|
||||
|
|
@ -1,122 +0,0 @@
|
|||
function [PredictedStateMean,PredictedStateVarianceSquareRoot,StateVectorMean,StateVectorVarianceSquareRoot] = gaussian_filter_bank(ReducedForm,obs,StateVectorMean,StateVectorVarianceSquareRoot,Q_lower_triangular_cholesky,H_lower_triangular_cholesky,H,DynareOptions)
|
||||
%
|
||||
% Computes the proposal with a gaussian approximation for importance
|
||||
% sampling
|
||||
% This proposal is a gaussian distribution calculated à la Kalman
|
||||
%
|
||||
% INPUTS
|
||||
% reduced_form_model [structure] Matlab's structure describing the reduced form model.
|
||||
% reduced_form_model.measurement.H [double] (pp x pp) variance matrix of measurement errors.
|
||||
% reduced_form_model.state.Q [double] (qq x qq) variance matrix of state errors.
|
||||
% reduced_form_model.state.dr [structure] output of resol.m.
|
||||
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
|
||||
%
|
||||
% OUTPUTS
|
||||
% LIK [double] scalar, likelihood
|
||||
% lik [double] vector, density of observations in each period.
|
||||
%
|
||||
% REFERENCES
|
||||
%
|
||||
% NOTES
|
||||
% The vector "lik" is used to evaluate the jacobian of the likelihood.
|
||||
% Copyright (C) 2009-2012 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
persistent init_flag2 mf0 mf1
|
||||
persistent number_of_state_variables number_of_observed_variables
|
||||
persistent number_of_structural_innovations
|
||||
|
||||
% Set local state space model (first-order approximation).
|
||||
ghx = ReducedForm.ghx;
|
||||
ghu = ReducedForm.ghu;
|
||||
% Set local state space model (second-order approximation).
|
||||
ghxx = ReducedForm.ghxx;
|
||||
ghuu = ReducedForm.ghuu;
|
||||
ghxu = ReducedForm.ghxu;
|
||||
|
||||
if any(any(isnan(ghx))) || any(any(isnan(ghu))) || any(any(isnan(ghxx))) || any(any(isnan(ghuu))) || any(any(isnan(ghxu))) || ...
|
||||
any(any(isinf(ghx))) || any(any(isinf(ghu))) || any(any(isinf(ghxx))) || any(any(isinf(ghuu))) || any(any(isinf(ghxu))) ...
|
||||
any(any(abs(ghx)>1e4)) || any(any(abs(ghu)>1e4)) || any(any(abs(ghxx)>1e4)) || any(any(abs(ghuu)>1e4)) || any(any(abs(ghxu)>1e4))
|
||||
ghx
|
||||
ghu
|
||||
ghxx
|
||||
ghuu
|
||||
ghxu
|
||||
end
|
||||
|
||||
constant = ReducedForm.constant;
|
||||
state_variables_steady_state = ReducedForm.state_variables_steady_state;
|
||||
|
||||
% Set persistent variables.
|
||||
if isempty(init_flag2)
|
||||
mf0 = ReducedForm.mf0;
|
||||
mf1 = ReducedForm.mf1;
|
||||
number_of_state_variables = length(mf0);
|
||||
number_of_observed_variables = length(mf1);
|
||||
number_of_structural_innovations = length(ReducedForm.Q);
|
||||
init_flag2 = 1;
|
||||
end
|
||||
|
||||
if DynareOptions.particle.proposal_approximation.cubature || DynareOptions.particle.proposal_approximation.montecarlo
|
||||
[nodes,weights] = spherical_radial_sigma_points(number_of_state_variables+number_of_structural_innovations) ;
|
||||
weights_c = weights ;
|
||||
elseif DynareOptions.particle.proposal_approximation.unscented
|
||||
[nodes,weights,weights_c] = unscented_sigma_points(number_of_state_variables+number_of_structural_innovations,DynareOptions);
|
||||
else
|
||||
error('Estimation: This approximation for the proposal is not implemented or unknown!')
|
||||
end
|
||||
|
||||
xbar = [StateVectorMean ; zeros(number_of_structural_innovations,1) ] ;
|
||||
sqr_Px = [ [ StateVectorVarianceSquareRoot zeros(number_of_state_variables,number_of_structural_innovations) ] ;
|
||||
[ zeros(number_of_structural_innovations,number_of_state_variables) Q_lower_triangular_cholesky ] ];
|
||||
sigma_points = bsxfun(@plus,xbar,sqr_Px*(nodes'));
|
||||
StateVectors = sigma_points(1:number_of_state_variables,:);
|
||||
epsilon = sigma_points(number_of_state_variables+1:number_of_state_variables+number_of_structural_innovations,:);
|
||||
yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
|
||||
tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
|
||||
PredictedStateMean = tmp(mf0,:)*weights ;
|
||||
PredictedObservedMean = tmp(mf1,:)*weights;
|
||||
|
||||
if DynareOptions.particle.proposal_approximation.cubature || DynareOptions.particle.proposal_approximation.montecarlo
|
||||
PredictedStateMean = sum(PredictedStateMean,2);
|
||||
PredictedObservedMean = sum(PredictedObservedMean,2);
|
||||
dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean)'.*sqrt(weights);
|
||||
dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean)'.*sqrt(weights);
|
||||
PredictedStateVarianceSquareRoot = chol(dState'*dState)';
|
||||
big_mat = [dObserved dState ; [H_lower_triangular_cholesky zeros(number_of_observed_variables,number_of_state_variables)] ];
|
||||
[mat1,mat] = qr2(big_mat,0);
|
||||
mat = mat';
|
||||
clear('mat1');
|
||||
PredictedObservedVarianceSquareRoot = mat(1:number_of_observed_variables,1:number_of_observed_variables);
|
||||
CovarianceObservedStateSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),1:number_of_observed_variables);
|
||||
StateVectorVarianceSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),number_of_observed_variables+(1:number_of_state_variables));
|
||||
PredictionError = obs - PredictedObservedMean;
|
||||
StateVectorMean = PredictedStateMean + (CovarianceObservedStateSquareRoot/PredictedObservedVarianceSquareRoot)*PredictionError;
|
||||
else
|
||||
dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean);
|
||||
dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean);
|
||||
PredictedStateVariance = dState*diag(weights_c)*dState';
|
||||
PredictedObservedVariance = dObserved*diag(weights_c)*dObserved' + H;
|
||||
PredictedStateAndObservedCovariance = dState*diag(weights_c)*dObserved';
|
||||
PredictedStateVarianceSquareRoot = chol(PredictedStateVariance)';
|
||||
PredictionError = obs - PredictedObservedMean;
|
||||
KalmanFilterGain = PredictedStateAndObservedCovariance/PredictedObservedVariance;
|
||||
StateVectorMean = PredictedStateMean + KalmanFilterGain*PredictionError;
|
||||
StateVectorVariance = PredictedStateVariance - KalmanFilterGain*PredictedObservedVariance*KalmanFilterGain';
|
||||
StateVectorVariance = .5*(StateVectorVariance+StateVectorVariance');
|
||||
StateVectorVarianceSquareRoot = reduced_rank_cholesky(StateVectorVariance)';
|
||||
end
|
||||
|
|
@ -1,58 +0,0 @@
|
|||
function IncrementalWeights = gaussian_mixture_densities(obs,StateMuPrior,StateSqrtPPrior,StateWeightsPrior,...
|
||||
StateMuPost,StateSqrtPPost,StateWeightsPost,...
|
||||
StateParticles,H,normconst,weigths1,weigths2,ReducedForm,DynareOptions)
|
||||
|
||||
%
|
||||
% Elements to calculate the importance sampling ratio
|
||||
%
|
||||
% INPUTS
|
||||
% reduced_form_model [structure] Matlab's structure describing the reduced form model.
|
||||
% reduced_form_model.measurement.H [double] (pp x pp) variance matrix of measurement errors.
|
||||
% reduced_form_model.state.Q [double] (qq x qq) variance matrix of state errors.
|
||||
% reduced_form_model.state.dr [structure] output of resol.m.
|
||||
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
|
||||
% start [integer] scalar, likelihood evaluation starts at 'start'.
|
||||
% smolyak_accuracy [integer] scalar.
|
||||
%
|
||||
% OUTPUTS
|
||||
% LIK [double] scalar, likelihood
|
||||
% lik [double] vector, density of observations in each period.
|
||||
%
|
||||
% REFERENCES
|
||||
%
|
||||
% NOTES
|
||||
% The vector "lik" is used to evaluate the jacobian of the likelihood.
|
||||
% Copyright (C) 2009-2012 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
% Compute the density of particles under the prior distribution
|
||||
[ras,ras,prior] = probability(StateMuPrior,StateSqrtPPrior,StateWeightsPrior,StateParticles) ;
|
||||
prior = prior' ;
|
||||
% Compute the density of particles under the proposal distribution
|
||||
[ras,ras,proposal] = probability(StateMuPost,StateSqrtPPost,StateWeightsPost,StateParticles) ;
|
||||
proposal = proposal' ;
|
||||
% Compute the density of the current observation conditionally to each particle
|
||||
yt_t_1_i = measurement_equations(StateParticles,ReducedForm,DynareOptions) ;
|
||||
eta_t_i = bsxfun(@minus,obs,yt_t_1_i)' ;
|
||||
yt_t_1 = sum(yt_t_1_i*weigths1,2) ;
|
||||
tmp = bsxfun(@minus,yt_t_1_i,yt_t_1) ;
|
||||
Pyy = bsxfun(@times,weigths2',tmp)*tmp' + H ;
|
||||
sqr_det = sqrt(det(Pyy)) ;
|
||||
foo = (eta_t_i/Pyy).*eta_t_i ;
|
||||
likelihood = exp(-0.5*sum(foo,2))/(normconst*sqr_det) + 1e-99 ;
|
||||
IncrementalWeights = likelihood.*prior./proposal ;
|
||||
|
||||
|
|
@ -1,225 +0,0 @@
|
|||
function [LIK,lik] = gaussian_mixture_filter(ReducedForm,Y,start,DynareOptions)
|
||||
% Evaluates the likelihood of a non-linear model approximating the state
|
||||
% variables distributions with gaussian mixtures. Gaussian Mixture allows reproducing
|
||||
% a wide variety of generalized distributions (when multimodal for instance).
|
||||
% Each gaussian distribution is obtained whether
|
||||
% - with a Smolyak quadrature à la Kronrod & Paterson (Heiss & Winschel 2010, Winschel & Kratzig 2010).
|
||||
% - with a radial-spherical cubature
|
||||
% - with scaled unscented sigma-points
|
||||
% A Sparse grid Kalman Filter is implemented on each component of the mixture,
|
||||
% which confers it a weight about current information.
|
||||
% Information on the current observables is then embodied in the proposal
|
||||
% distribution in which we draw particles, which allows
|
||||
% - reaching a greater precision relatively to a standard particle filter,
|
||||
% - reducing the number of particles needed,
|
||||
% - still being faster.
|
||||
%
|
||||
%
|
||||
% INPUTS
|
||||
% reduced_form_model [structure] Matlab's structure describing the reduced form model.
|
||||
% reduced_form_model.measurement.H [double] (pp x pp) variance matrix of measurement errors.
|
||||
% reduced_form_model.state.Q [double] (qq x qq) variance matrix of state errors.
|
||||
% reduced_form_model.state.dr [structure] output of resol.m.
|
||||
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
|
||||
% start [integer] scalar, likelihood evaluation starts at 'start'.
|
||||
%
|
||||
% OUTPUTS
|
||||
% LIK [double] scalar, likelihood
|
||||
% lik [double] vector, density of observations in each period.
|
||||
%
|
||||
% REFERENCES
|
||||
%
|
||||
% Van der Meerwe & Wan, Gaussian Mixture Sigma-Point Particle Filters for Sequential
|
||||
% Probabilistic Inference in Dynamic State-Space Models.
|
||||
% Heiss & Winschel, 2010, Journal of Applied Economics.
|
||||
% Winschel & Kratzig, 2010, Econometrica.
|
||||
%
|
||||
% NOTES
|
||||
% The vector "lik" is used to evaluate the jacobian of the likelihood.
|
||||
% Copyright (C) 2009-2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
|
||||
persistent init_flag mf0 mf1 Gprime Gsecond
|
||||
persistent nodes weights weights_c I J G number_of_particles
|
||||
persistent sample_size number_of_state_variables number_of_observed_variables number_of_structural_innovations
|
||||
|
||||
% Set default
|
||||
if isempty(start)
|
||||
start = 1;
|
||||
end
|
||||
|
||||
% Set persistent variables.
|
||||
if isempty(init_flag)
|
||||
mf0 = ReducedForm.mf0;
|
||||
mf1 = ReducedForm.mf1;
|
||||
sample_size = size(Y,2);
|
||||
number_of_state_variables = length(mf0);
|
||||
number_of_observed_variables = length(mf1);
|
||||
number_of_structural_innovations = length(ReducedForm.Q);
|
||||
G = DynareOptions.particle.mixture_state_variables; % number of GM components in state
|
||||
I = DynareOptions.particle.mixture_structural_shocks ; % number of GM components in structural noise
|
||||
J = DynareOptions.particle.mixture_measurement_shocks ; % number of GM components in observation noise
|
||||
Gprime = G*I ;
|
||||
Gsecond = G*I*J ;
|
||||
number_of_particles = DynareOptions.particle.number_of_particles;
|
||||
init_flag = 1;
|
||||
end
|
||||
|
||||
SampleWeights = ones(Gsecond,1)/Gsecond ;
|
||||
|
||||
% compute gaussian quadrature nodes and weights on states and shocks
|
||||
if isempty(nodes)
|
||||
if DynareOptions.particle.distribution_approximation.cubature
|
||||
[nodes,weights] = spherical_radial_sigma_points(number_of_state_variables);
|
||||
weights_c = weights;
|
||||
elseif DynareOptions.particle.distribution_approximation.unscented
|
||||
[nodes,weights,weights_c] = unscented_sigma_points(number_of_state_variables,DynareOptions);
|
||||
else
|
||||
if ~DynareOptions.particle.distribution_approximation.montecarlo
|
||||
error('Estimation: This approximation for the proposal is not implemented or unknown!')
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
if DynareOptions.particle.distribution_approximation.montecarlo
|
||||
set_dynare_seed('default');
|
||||
SampleWeights = 1/number_of_particles ;
|
||||
end
|
||||
|
||||
% Get covariance matrices
|
||||
Q = ReducedForm.Q;
|
||||
H = ReducedForm.H;
|
||||
if isempty(H)
|
||||
H = 0;
|
||||
H_lower_triangular_cholesky = 0;
|
||||
else
|
||||
H_lower_triangular_cholesky = reduced_rank_cholesky(H)';
|
||||
end
|
||||
Q_lower_triangular_cholesky = reduced_rank_cholesky(Q)';
|
||||
|
||||
% Initialize all matrices
|
||||
StateWeights = ones(1,G)/G ;
|
||||
StateMu = ReducedForm.StateVectorMean*ones(1,G) ;
|
||||
StateSqrtP = zeros(number_of_state_variables,number_of_state_variables,G) ;
|
||||
for g=1:G
|
||||
StateSqrtP(:,:,g) = reduced_rank_cholesky(ReducedForm.StateVectorVariance)' ;
|
||||
end
|
||||
|
||||
StructuralShocksWeights = ones(1,I)/I ;
|
||||
StructuralShocksMu = zeros(number_of_structural_innovations,I) ;
|
||||
StructuralShocksSqrtP = zeros(number_of_structural_innovations,number_of_structural_innovations,I) ;
|
||||
for i=1:I
|
||||
StructuralShocksSqrtP(:,:,i) = Q_lower_triangular_cholesky ;
|
||||
end
|
||||
|
||||
ObservationShocksWeights = ones(1,J)/J ;
|
||||
ObservationShocksMu = zeros(number_of_observed_variables,J) ;
|
||||
ObservationShocksSqrtP = zeros(number_of_observed_variables,number_of_observed_variables,J) ;
|
||||
for j=1:J
|
||||
ObservationShocksSqrtP(:,:,j) = H_lower_triangular_cholesky ;
|
||||
end
|
||||
|
||||
StateWeightsPrior = zeros(1,Gprime) ;
|
||||
StateMuPrior = zeros(number_of_state_variables,Gprime) ;
|
||||
StateSqrtPPrior = zeros(number_of_state_variables,number_of_state_variables,Gprime) ;
|
||||
|
||||
StateWeightsPost = zeros(1,Gsecond) ;
|
||||
StateMuPost = zeros(number_of_state_variables,Gsecond) ;
|
||||
StateSqrtPPost = zeros(number_of_state_variables,number_of_state_variables,Gsecond) ;
|
||||
|
||||
%estimate = zeros(sample_size,number_of_state_variables,3) ;
|
||||
const_lik = (2*pi)^(.5*number_of_observed_variables) ;
|
||||
|
||||
ks = 0 ;
|
||||
lik = NaN(sample_size,1);
|
||||
LIK = NaN;
|
||||
for t=1:sample_size
|
||||
% Build the proposal joint quadratures of Gaussian on states, structural
|
||||
% shocks and observation shocks based on each combination of mixtures
|
||||
for i=1:I
|
||||
for j=1:J
|
||||
for g=1:G ;
|
||||
a = g + (j-1)*G ;
|
||||
b = a + (i-1)*Gprime ;
|
||||
[StateMuPrior(:,a),StateSqrtPPrior(:,:,a),StateWeightsPrior(1,a),...
|
||||
StateMuPost(:,b),StateSqrtPPost(:,:,b),StateWeightsPost(1,b)] =...
|
||||
gaussian_mixture_filter_bank(ReducedForm,Y(:,t),StateMu(:,g),StateSqrtP(:,:,g),StateWeights(1,g),...
|
||||
StructuralShocksMu(:,i),StructuralShocksSqrtP(:,:,i),StructuralShocksWeights(1,i),...
|
||||
ObservationShocksMu(:,j),ObservationShocksSqrtP(:,:,j),ObservationShocksWeights(1,j),...
|
||||
H,H_lower_triangular_cholesky,const_lik,DynareOptions) ;
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
% Normalize weights
|
||||
StateWeightsPrior = StateWeightsPrior/sum(StateWeightsPrior,2) ;
|
||||
StateWeightsPost = StateWeightsPost/sum(StateWeightsPost,2) ;
|
||||
|
||||
if DynareOptions.particle.distribution_approximation.cubature || DynareOptions.particle.distribution_approximation.unscented
|
||||
for i=1:Gsecond
|
||||
StateParticles = bsxfun(@plus,StateMuPost(:,i),StateSqrtPPost(:,:,i)*nodes') ;
|
||||
IncrementalWeights = gaussian_mixture_densities(Y(:,t),StateMuPrior,StateSqrtPPrior,StateWeightsPrior,...
|
||||
StateMuPost,StateSqrtPPost,StateWeightsPost,...
|
||||
StateParticles,H,const_lik,weights,weights_c,ReducedForm,DynareOptions) ;
|
||||
SampleWeights(i) = sum(StateWeightsPost(i)*weights.*IncrementalWeights) ;
|
||||
end
|
||||
SumSampleWeights = sum(SampleWeights) ;
|
||||
lik(t) = log(SumSampleWeights) ;
|
||||
SampleWeights = SampleWeights./SumSampleWeights ;
|
||||
[ras,SortedRandomIndx] = sort(rand(1,Gsecond));
|
||||
SortedRandomIndx = SortedRandomIndx(1:G);
|
||||
indx = index_resample(0,SampleWeights,DynareOptions) ;
|
||||
indx = indx(SortedRandomIndx) ;
|
||||
StateMu = StateMuPost(:,indx);
|
||||
StateSqrtP = StateSqrtPPost(:,:,indx);
|
||||
StateWeights = ones(1,G)/G ;
|
||||
else
|
||||
% Sample particle in the proposal distribution, ie the posterior state GM
|
||||
StateParticles = importance_sampling(StateMuPost,StateSqrtPPost,StateWeightsPost',number_of_particles) ;
|
||||
% Compute prior, proposal and likelihood of particles
|
||||
IncrementalWeights = gaussian_mixture_densities(Y(:,t),StateMuPrior,StateSqrtPPrior,StateWeightsPrior,...
|
||||
StateMuPost,StateSqrtPPost,StateWeightsPost,...
|
||||
StateParticles,H,const_lik,1/number_of_particles,...
|
||||
1/number_of_particles,ReducedForm,DynareOptions) ;
|
||||
% calculate importance weights of particles
|
||||
SampleWeights = SampleWeights.*IncrementalWeights ;
|
||||
SumSampleWeights = sum(SampleWeights,1) ;
|
||||
SampleWeights = SampleWeights./SumSampleWeights ;
|
||||
lik(t) = log(SumSampleWeights) ;
|
||||
% First possible state point estimates
|
||||
%estimate(t,:,1) = SampleWeights*StateParticles' ;
|
||||
% Resampling if needed of required
|
||||
Neff = 1/sum(bsxfun(@power,SampleWeights,2)) ;
|
||||
if (DynareOptions.particle.resampling.status.generic && Neff<.5*sample_size) || DynareOptions.particle.resampling.status.systematic
|
||||
ks = ks + 1 ;
|
||||
StateParticles = resample(StateParticles',SampleWeights,DynareOptions)' ;
|
||||
StateVectorMean = mean(StateParticles,2) ;
|
||||
StateVectorVarianceSquareRoot = reduced_rank_cholesky( (StateParticles*StateParticles')/number_of_particles - StateVectorMean*(StateVectorMean') )';
|
||||
SampleWeights = 1/number_of_particles ;
|
||||
elseif DynareOptions.particle.resampling.status.none
|
||||
StateVectorMean = StateParticles*sampleWeights ;
|
||||
temp = sqrt(SampleWeights').*StateParticles ;
|
||||
StateVectorVarianceSquareRoot = reduced_rank_cholesky( temp*temp' - StateVectorMean*(StateVectorMean') )';
|
||||
end
|
||||
% Use the information from particles to update the gaussian mixture on state variables
|
||||
[StateMu,StateSqrtP,StateWeights] = fit_gaussian_mixture(StateParticles,StateMu,StateSqrtP,StateWeights,0.001,10,1) ;
|
||||
%estimate(t,:,3) = StateWeights*StateMu' ;
|
||||
end
|
||||
end
|
||||
|
||||
LIK = -sum(lik(start:end)) ;
|
||||
|
|
@ -1,138 +0,0 @@
|
|||
function [StateMuPrior,StateSqrtPPrior,StateWeightsPrior,StateMuPost,StateSqrtPPost,StateWeightsPost] =...
|
||||
gaussian_mixture_filter_bank(ReducedForm,obs,StateMu,StateSqrtP,StateWeights,...
|
||||
StructuralShocksMu,StructuralShocksSqrtP,StructuralShocksWeights,...
|
||||
ObservationShocksMu,ObservationShocksSqrtP,ObservationShocksWeights,...
|
||||
H,H_lower_triangular_cholesky,normfactO,DynareOptions)
|
||||
%
|
||||
% Computes the proposal with a gaussian approximation for importance
|
||||
% sampling
|
||||
% This proposal is a gaussian distribution calculated à la Kalman
|
||||
%
|
||||
% INPUTS
|
||||
% reduced_form_model [structure] Matlab's structure describing the reduced form model.
|
||||
% reduced_form_model.measurement.H [double] (pp x pp) variance matrix of measurement errors.
|
||||
% reduced_form_model.state.Q [double] (qq x qq) variance matrix of state errors.
|
||||
% reduced_form_model.state.dr [structure] output of resol.m.
|
||||
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
|
||||
%
|
||||
% OUTPUTS
|
||||
% LIK [double] scalar, likelihood
|
||||
% lik [double] vector, density of observations in each period.
|
||||
%
|
||||
% REFERENCES
|
||||
%
|
||||
% NOTES
|
||||
% The vector "lik" is used to evaluate the jacobian of the likelihood.
|
||||
% Copyright (C) 2009-2012 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
|
||||
|
||||
persistent init_flag2 mf0 mf1 %nodes3 weights3 weights_c3
|
||||
persistent number_of_state_variables number_of_observed_variables
|
||||
persistent number_of_structural_innovations
|
||||
|
||||
% Set local state space model (first-order approximation).
|
||||
ghx = ReducedForm.ghx;
|
||||
ghu = ReducedForm.ghu;
|
||||
% Set local state space model (second-order approximation).
|
||||
ghxx = ReducedForm.ghxx;
|
||||
ghuu = ReducedForm.ghuu;
|
||||
ghxu = ReducedForm.ghxu;
|
||||
|
||||
if any(any(isnan(ghx))) || any(any(isnan(ghu))) || any(any(isnan(ghxx))) || any(any(isnan(ghuu))) || any(any(isnan(ghxu))) || ...
|
||||
any(any(isinf(ghx))) || any(any(isinf(ghu))) || any(any(isinf(ghxx))) || any(any(isinf(ghuu))) || any(any(isinf(ghxu))) ...
|
||||
any(any(abs(ghx)>1e4)) || any(any(abs(ghu)>1e4)) || any(any(abs(ghxx)>1e4)) || any(any(abs(ghuu)>1e4)) || any(any(abs(ghxu)>1e4))
|
||||
ghx
|
||||
ghu
|
||||
ghxx
|
||||
ghuu
|
||||
ghxu
|
||||
end
|
||||
|
||||
constant = ReducedForm.constant;
|
||||
state_variables_steady_state = ReducedForm.state_variables_steady_state;
|
||||
|
||||
% Set persistent variables.
|
||||
if isempty(init_flag2)
|
||||
mf0 = ReducedForm.mf0;
|
||||
mf1 = ReducedForm.mf1;
|
||||
number_of_state_variables = length(mf0);
|
||||
number_of_observed_variables = length(mf1);
|
||||
number_of_structural_innovations = length(ReducedForm.Q);
|
||||
init_flag2 = 1;
|
||||
end
|
||||
|
||||
numb = number_of_state_variables+number_of_structural_innovations ;
|
||||
|
||||
if DynareOptions.particle.proposal_approximation.cubature
|
||||
[nodes3,weights3] = spherical_radial_sigma_points(numb);
|
||||
weights_c3 = weights3;
|
||||
elseif DynareOptions.particle.proposal_approximation.unscented
|
||||
[nodes3,weights3,weights_c3] = unscented_sigma_points(numb,DynareOptions);
|
||||
else
|
||||
error('Estimation: This approximation for the proposal is not implemented or unknown!')
|
||||
end
|
||||
|
||||
epsilon = bsxfun(@plus,StructuralShocksSqrtP*nodes3(:,number_of_state_variables+1:number_of_state_variables+number_of_structural_innovations)',StructuralShocksMu) ;
|
||||
StateVectors = bsxfun(@plus,StateSqrtP*nodes3(:,1:number_of_state_variables)',StateMu);
|
||||
yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
|
||||
tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
|
||||
PredictedStateMean = tmp(mf0,:)*weights3;
|
||||
PredictedObservedMean = tmp(mf1,:)*weights3;
|
||||
|
||||
if DynareOptions.particle.proposal_approximation.cubature
|
||||
PredictedStateMean = sum(PredictedStateMean,2);
|
||||
PredictedObservedMean = sum(PredictedObservedMean,2);
|
||||
dState = (bsxfun(@minus,tmp(mf0,:),PredictedStateMean)').*sqrt(weights3);
|
||||
dObserved = (bsxfun(@minus,tmp(mf1,:),PredictedObservedMean)').*sqrt(weights3);
|
||||
PredictedStateVariance = dState'*dState;
|
||||
big_mat = [dObserved dState ; [H_lower_triangular_cholesky zeros(number_of_observed_variables,number_of_state_variables)] ];
|
||||
[mat1,mat] = qr2(big_mat,0);
|
||||
mat = mat';
|
||||
clear('mat1');
|
||||
PredictedObservedVarianceSquareRoot = mat(1:number_of_observed_variables,1:number_of_observed_variables);
|
||||
CovarianceObservedStateSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),1:number_of_observed_variables);
|
||||
StateVectorVarianceSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),number_of_observed_variables+(1:number_of_state_variables));
|
||||
iPredictedObservedVarianceSquareRoot = inv(PredictedObservedVarianceSquareRoot);
|
||||
iPredictedObservedVariance = iPredictedObservedVarianceSquareRoot'*iPredictedObservedVarianceSquareRoot;
|
||||
sqrdet = 1/sqrt(det(iPredictedObservedVariance));
|
||||
PredictionError = obs - PredictedObservedMean;
|
||||
StateVectorMean = PredictedStateMean + CovarianceObservedStateSquareRoot*iPredictedObservedVarianceSquareRoot*PredictionError;
|
||||
else
|
||||
dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean);
|
||||
dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean);
|
||||
PredictedStateVariance = dState*diag(weights_c3)*dState';
|
||||
PredictedObservedVariance = dObserved*diag(weights_c3)*dObserved' + H;
|
||||
PredictedStateAndObservedCovariance = dState*diag(weights_c3)*dObserved';
|
||||
sqrdet = sqrt(det(PredictedObservedVariance)) ;
|
||||
iPredictedObservedVariance = inv(PredictedObservedVariance);
|
||||
PredictionError = obs - PredictedObservedMean;
|
||||
KalmanFilterGain = PredictedStateAndObservedCovariance*iPredictedObservedVariance;
|
||||
StateVectorMean = PredictedStateMean + KalmanFilterGain*PredictionError;
|
||||
StateVectorVariance = PredictedStateVariance - KalmanFilterGain*PredictedObservedVariance*KalmanFilterGain';
|
||||
StateVectorVariance = .5*(StateVectorVariance+StateVectorVariance');
|
||||
StateVectorVarianceSquareRoot = reduced_rank_cholesky(StateVectorVariance)';
|
||||
end
|
||||
|
||||
data_lik_GM_g = exp(-0.5*PredictionError'*iPredictedObservedVariance*PredictionError)/abs(normfactO*sqrdet) + 1e-99;
|
||||
StateMuPrior = PredictedStateMean ;
|
||||
StateSqrtPPrior = reduced_rank_cholesky(PredictedStateVariance)';
|
||||
StateWeightsPrior = StateWeights*StructuralShocksWeights;
|
||||
StateMuPost = StateVectorMean;
|
||||
StateSqrtPPost = StateVectorVarianceSquareRoot;
|
||||
StateWeightsPost = StateWeightsPrior*ObservationShocksWeights*data_lik_GM_g ;
|
||||
|
|
@ -1,29 +0,0 @@
|
|||
function State_Particles = importance_sampling(StateMuPost,StateSqrtPPost,StateWeightsPost,numP)
|
||||
|
||||
% Copyright (C) 2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
[Xdim,Gsecond] = size(StateMuPost) ;
|
||||
u = rand(numP,1);
|
||||
[Nc,comp] = histc(u, cumsum([0; StateWeightsPost]));
|
||||
State_Particles = zeros(Xdim,numP);
|
||||
for k=1:Gsecond
|
||||
idx = bsxfun(@eq,comp,k*ones(size(comp))) ;
|
||||
State_Particles(:,idx) = StateSqrtPPost(:,:,k)*randn(Xdim,Nc(k));
|
||||
end
|
||||
State_Particles= State_Particles + StateMuPost(:,comp);
|
||||
|
||||
|
|
@ -1,72 +0,0 @@
|
|||
function resampling_index = index_resample(particles,weights,DynareOptions)
|
||||
% Resamples particles.
|
||||
|
||||
%@info:
|
||||
%! @deftypefn {Function File} {@var{indx} =} resample (@var{weights}, @var{method})
|
||||
%! @anchor{particle/resample}
|
||||
%! @sp 1
|
||||
%! Resamples particles.
|
||||
%! @sp 2
|
||||
%! @strong{Inputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item weights
|
||||
%! n*1 vector of doubles, particles' weights.
|
||||
%! @item method
|
||||
%! string equal to 'residual' or 'traditional'.
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{Outputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item indx
|
||||
%! n*1 vector of intergers, indices.
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{This function is called by:}
|
||||
%! @sp 1
|
||||
%! @ref{particle/sequantial_importance_particle_filter}
|
||||
%! @sp 2
|
||||
%! @strong{This function calls:}
|
||||
%! @sp 1
|
||||
%! @ref{residual_resampling}, @ref{traditional_resampling}
|
||||
%! @sp 2
|
||||
%! @end deftypefn
|
||||
%@eod:
|
||||
|
||||
% Copyright (C) 2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
defaultmethod = 1; % For residual based method set this variable equal to 0.
|
||||
|
||||
if defaultmethod
|
||||
if DynareOptions.particle.resampling.method.kitagawa
|
||||
resampling_index = traditional_resampling(particles,weights,rand);
|
||||
elseif DynareOptions.particle.resampling.method.stratified
|
||||
resampling_index = traditional_resampling(particles,weights,rand(size(weights)));
|
||||
else
|
||||
error('Unknow sampling method!')
|
||||
end
|
||||
else
|
||||
if DynareOptions.particle.resampling.method.kitagawa
|
||||
resampled_particles = residual_resampling(particles,weights,rand);
|
||||
elseif DynareOptions.particle.resampling.method.stratified
|
||||
resampled_particles = residual_resampling(particles,weights,rand(size(weights)));
|
||||
else
|
||||
error('Unknown sampling method!')
|
||||
end
|
||||
end
|
||||
|
|
@ -1,275 +0,0 @@
|
|||
function [y,y_] = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,a,b,c)%yhat_,ss)
|
||||
|
||||
%@info:
|
||||
%! @deftypefn {Function File} {@var{y}, @var{y_} =} local_state_equation_2 (@var{yhat},@var{epsilon}, @var{ghx}, @var{ghu}, @var{constant}, @var{ghxx}, @var{ghuu}, @var{ghxu}, @var{yhat_}, @var{ss})
|
||||
%! @anchor{particle/local_state_space_iteration_2}
|
||||
%! @sp 1
|
||||
%! Given the states (y) and structural innovations (epsilon), this routine computes the level of selected endogenous variables when the
|
||||
%! model is approximated by an order two taylor expansion around the deterministic steady state. Depending on the number of input/output
|
||||
%! argument the pruning algorithm advocated by C. Sims is used or not (this version should not be used if the selected endogenous variables
|
||||
%! are not the states of the model).
|
||||
%!
|
||||
%! @sp 2
|
||||
%! @strong{Inputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item yhat
|
||||
%! n*1 vector of doubles, initial condition, where n is the number of state variables.
|
||||
%! @item epsilon
|
||||
%! q*1 vector of doubles, structural innovations.
|
||||
%! @item ghx
|
||||
%! m*n matrix of doubles, restricted dr.ghx where we only consider the lines corresponding to a subset of endogenous variables.
|
||||
%! @item ghu
|
||||
%! m*q matrix of doubles, restricted dr.ghu where we only consider the lines corresponding to a subset of endogenous variables.
|
||||
%! @item constant
|
||||
%! m*1 vector of doubles, deterministic steady state plus second order correction for a subset of endogenous variables.
|
||||
%! @item ghxx
|
||||
%! m*n² matrix of doubles, restricted dr.ghxx where we only consider the lines corresponding to a subset of endogenous variables.
|
||||
%! @item ghuu
|
||||
%! m*q² matrix of doubles, restricted dr.ghuu where we only consider the lines corresponding to a subset of endogenous variables.
|
||||
%! @item ghxu
|
||||
%! m*(nq) matrix of doubles, subset of dr.ghxu where we only consider the lines corresponding to a subset of endogenous variables.
|
||||
%! @item yhat_
|
||||
%! n*1 vector of doubles, spurious states for the pruning version.
|
||||
%! @item ss
|
||||
%! n*1 vector of doubles, steady state for the states.
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{Outputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item y
|
||||
%! m*1 vector of doubles, selected endogenous variables.
|
||||
%! @item y_
|
||||
%! m*1 vector of doubles, update of the latent variables needed for the pruning version (first order update).
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{Remarks}
|
||||
%! @sp 1
|
||||
%! [1] If the function has 10 input arguments then it must have 2 output arguments (pruning version).
|
||||
%! @sp 1
|
||||
%! [2] If the function has 08 input arguments then it must have 1 output argument.
|
||||
%! @sp 2
|
||||
%! @strong{This function is called by:}
|
||||
%! @sp 2
|
||||
%! @strong{This function calls:}
|
||||
%!
|
||||
%!
|
||||
%! @end deftypefn
|
||||
%@eod:
|
||||
|
||||
% Copyright (C) 2011-2012 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
% AUTHOR(S) stephane DOT adjemian AT univ DASH lemans DOT fr
|
||||
% frederic DOT karame AT univ DASH evry DOT fr
|
||||
|
||||
if nargin==9
|
||||
pruning = 0; numthreads = a;
|
||||
if nargout>1
|
||||
error('local_state_space_iteration_2:: Numbers of input and output argument are inconsistent!')
|
||||
end
|
||||
elseif nargin==11
|
||||
pruning = 1; numthreads = c; yhat_ = a; ss = b;
|
||||
if nargout~=2
|
||||
error('local_state_space_iteration_2:: Numbers of input and output argument are inconsistent!')
|
||||
end
|
||||
else
|
||||
error('local_state_space_iteration_2:: Wrong number of input arguments!')
|
||||
end
|
||||
|
||||
number_of_threads = numthreads;
|
||||
|
||||
switch pruning
|
||||
case 0
|
||||
for i =1:size(yhat,2)
|
||||
y(:,i) = constant + ghx*yhat(:,i) + ghu*epsilon(:,i) ...
|
||||
+ A_times_B_kronecker_C(.5*ghxx,yhat(:,i),number_of_threads) ...
|
||||
+ A_times_B_kronecker_C(.5*ghuu,epsilon(:,i),number_of_threads) ...
|
||||
+ A_times_B_kronecker_C(ghxu,yhat(:,i),epsilon(:,i),number_of_threads);
|
||||
end
|
||||
case 1
|
||||
for i =1:size(yhat,2)
|
||||
y(:,i) = constant + ghx*yhat(:,i) + ghu*epsilon(:,i) ...
|
||||
+ A_times_B_kronecker_C(.5*ghxx,yhat_(:,i),number_of_threads) ...
|
||||
+ A_times_B_kronecker_C(.5*ghuu,epsilon(:,i),number_of_threads) ...
|
||||
+ A_times_B_kronecker_C(ghxu,yhat_(:,i),epsilon(:,i),number_of_threads);
|
||||
end
|
||||
y_ = ghx*yhat_+ghu*epsilon;
|
||||
y_ = bsxfun(@plus,y_,ss);
|
||||
end
|
||||
|
||||
%@test:1
|
||||
%$ n = 2;
|
||||
%$ q = 3;
|
||||
%$
|
||||
%$ yhat = zeros(n,1);
|
||||
%$ epsilon = zeros(q,1);
|
||||
%$ ghx = rand(n,n);
|
||||
%$ ghu = rand(n,q);
|
||||
%$ constant = ones(n,1);
|
||||
%$ ghxx = rand(n,n*n);
|
||||
%$ ghuu = rand(n,q*q);
|
||||
%$ ghxu = rand(n,n*q);
|
||||
%$ yhat_ = zeros(n,1);
|
||||
%$ ss = ones(n,1);
|
||||
%$
|
||||
%$ % Call the tested routine.
|
||||
%$ for i=1:10
|
||||
%$ y1 = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,1);
|
||||
%$ [y2,y2_] = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,ss,1);
|
||||
%$ end
|
||||
%$
|
||||
%$ % Check the results.
|
||||
%$ t(1) = dassert(y1,ones(n,1));
|
||||
%$ t(2) = dassert(y2,ones(n,1));
|
||||
%$ t(3) = dassert(y2_,ones(n,1));
|
||||
%$ T = all(t);
|
||||
%@eof:1
|
||||
|
||||
%@test:2
|
||||
%$ old_path = pwd;
|
||||
%$ cd([fileparts(which('dynare')) '/../tests/']);
|
||||
%$ dynare('dsge_base2');
|
||||
%$ load dsge_base2;
|
||||
%$ cd(old_path);
|
||||
%$ dr = oo_.dr;
|
||||
%$ clear('oo_','options_','M_');
|
||||
%$ delete([fileparts(which('dynare')) '/../tests/dsge_base2.mat']);
|
||||
%$ istates = dr.nstatic+(1:dr.npred);
|
||||
%$ n = dr.npred;
|
||||
%$ q = size(dr.ghu,2);
|
||||
%$ yhat = zeros(n,1);
|
||||
%$ epsilon = zeros(q,1);
|
||||
%$ ghx = dr.ghx(istates,:);
|
||||
%$ ghu = dr.ghu(istates,:);
|
||||
%$ constant = dr.ys(istates,:)+dr.ghs2(istates,:);
|
||||
%$ ghxx = dr.ghxx(istates,:);
|
||||
%$ ghuu = dr.ghuu(istates,:);
|
||||
%$ ghxu = dr.ghxu(istates,:);
|
||||
%$ yhat_ = zeros(n,1);
|
||||
%$ ss = dr.ys(istates,:);
|
||||
%$
|
||||
%$ t = ones(2,1);
|
||||
%$
|
||||
%$ % Call the tested routine.
|
||||
%$ try
|
||||
%$ y1 = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,1);
|
||||
%$ catch
|
||||
%$ t(1) = 0;
|
||||
%$ end
|
||||
%$ try
|
||||
%$ [y2,y2_] = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,ss,1);
|
||||
%$ catch
|
||||
%$ t(2) = 0;
|
||||
%$ end
|
||||
%$
|
||||
%$ % Check the results.
|
||||
%$ T = all(t);
|
||||
%@eof:2
|
||||
|
||||
%@test:3
|
||||
%$ Bohrbug = 1; % A bug that manifests reliably under a possibly unknown but well-defined set of conditions.
|
||||
%$ if ~Bohrbug
|
||||
%$ n = 2;
|
||||
%$ q = 3;
|
||||
%$
|
||||
%$ yhat = .01*randn(n,1);
|
||||
%$ epsilon = .001*randn(q,1);
|
||||
%$ ghx = rand(n,n);
|
||||
%$ ghu = rand(n,q);
|
||||
%$ constant = ones(n,1);
|
||||
%$ ghxx = rand(n,n*n);
|
||||
%$ ghuu = rand(n,q*q);
|
||||
%$ ghxu = rand(n,n*q);
|
||||
%$ yhat_ = zeros(n,1);
|
||||
%$ ss = ones(n,1);
|
||||
%$
|
||||
%$ % Call the tested routine (mex version).
|
||||
%$ y1a = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,1);
|
||||
%$ [y2a,y2a_] = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,ss,1);
|
||||
%$
|
||||
%$ % Call the tested routine (matlab version)
|
||||
%$ path_to_mex = fileparts(which(['qmc_sequence.' mexext]));
|
||||
%$ where_am_i_coming_from = pwd;
|
||||
%$ cd(path_to_mex);
|
||||
%$ tar('local_state_space_iteration_2.tar',['local_state_space_iteration_2.' mexext]);
|
||||
%$ cd(where_am_i_coming_from);
|
||||
%$ dynare_config([],0);
|
||||
%$ y1b = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,1);
|
||||
%$ [y2b,y2b_] = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,ss,1);
|
||||
%$ cd(path_to_mex);
|
||||
%$ untar('local_state_space_iteration_2.tar');
|
||||
%$ delete('local_state_space_iteration_2.tar');
|
||||
%$ cd(where_am_i_coming_from);
|
||||
%$ dynare_config([],0);
|
||||
%$ % Check the results.
|
||||
%$ t(1) = dassert(y1a,y1b);
|
||||
%$ t(2) = dassert(y2a,y2b);
|
||||
%$ t(3) = dassert(y2a_,y2b_);
|
||||
%$ T = all(t);
|
||||
%$ else
|
||||
%$ t(1) = 1;
|
||||
%$ T = all(t);
|
||||
%$ end
|
||||
%@eof:3
|
||||
|
||||
|
||||
%@test:4
|
||||
%$ % TIMING TEST (parallelization with openmp)
|
||||
%$ old_path = pwd;
|
||||
%$ cd([fileparts(which('dynare')) '/../tests/']);
|
||||
%$ dynare('dsge_base2');
|
||||
%$ load dsge_base2;
|
||||
%$ cd(old_path);
|
||||
%$ dr = oo_.dr;
|
||||
%$ clear('oo_','options_','M_');
|
||||
%$ delete([fileparts(which('dynare')) '/../tests/dsge_base2.mat']);
|
||||
%$ istates = dr.nstatic+(1:dr.npred);
|
||||
%$ n = dr.npred;
|
||||
%$ q = size(dr.ghu,2);
|
||||
%$ yhat = zeros(n,10000000);
|
||||
%$ epsilon = zeros(q,10000000);
|
||||
%$ ghx = dr.ghx(istates,:);
|
||||
%$ ghu = dr.ghu(istates,:);
|
||||
%$ constant = dr.ys(istates,:)+dr.ghs2(istates,:);
|
||||
%$ ghxx = dr.ghxx(istates,:);
|
||||
%$ ghuu = dr.ghuu(istates,:);
|
||||
%$ ghxu = dr.ghxu(istates,:);
|
||||
%$ yhat_ = zeros(n,10000000);
|
||||
%$ ss = dr.ys(istates,:);
|
||||
%$
|
||||
%$ t = NaN(4,1);
|
||||
%$ tic, for i=1:10, y1 = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,1); end
|
||||
%$ t1 = toc;
|
||||
%$ tic, for i=1:10, y2 = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,2); end
|
||||
%$ t2 = toc;
|
||||
%$ t(1) = dassert(y1,y2,1e-15); clear('y1');
|
||||
%$ tic, for i=1:10, y3 = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,3); end
|
||||
%$ t3 = toc;
|
||||
%$ t(2) = dassert(y2,y3,1e-15); clear('y2');
|
||||
%$ tic, for i=1:10, y4 = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,4); end
|
||||
%$ t4 = toc;
|
||||
%$ t(3) = dassert(y4,y3,1e-15); clear('y3','y4');
|
||||
%$ t(4) = (t1>t2) && (t2>t3) && (t3>t4);
|
||||
%$ if ~t(4)
|
||||
%$ disp('Timmings:')
|
||||
%$ [t1, t2, t3, t4]
|
||||
%$ end
|
||||
%$ % Check the results.
|
||||
%$ T = all(t);
|
||||
%@eof:4
|
||||
|
|
@ -1,33 +0,0 @@
|
|||
function measure = measurement_equations(StateVectors,ReducedForm,DynareOptions)
|
||||
|
||||
% Copyright (C) 2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
mf1 = ReducedForm.mf1;
|
||||
ghx = ReducedForm.ghx(mf1,:);
|
||||
ghu = ReducedForm.ghu(mf1,:);
|
||||
ghxx = ReducedForm.ghxx(mf1,:);
|
||||
ghuu = ReducedForm.ghuu(mf1,:);
|
||||
ghxu = ReducedForm.ghxu(mf1,:);
|
||||
constant = ReducedForm.constant(mf1,:);
|
||||
state_variables_steady_state = ReducedForm.state_variables_steady_state;
|
||||
number_of_structural_innovations = length(ReducedForm.Q);
|
||||
yhat = bsxfun(@minus,StateVectors,state_variables_steady_state) ;
|
||||
measure = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,size(yhat,2)),ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
|
||||
|
||||
|
||||
|
||||
|
|
@ -1,72 +0,0 @@
|
|||
function new_particles = multivariate_smooth_resampling(particles,weights)
|
||||
% Smooth Resampling of the particles.
|
||||
|
||||
%@info:
|
||||
%! @deftypefn {Function File} {@var{new_particles} =} multivariate_smooth_resampling (@var{weights}, @var{particles}, @var{number_of_new_particles}, @var{number_of_partitions})
|
||||
%! @anchor{particle/multivariate_smooth_resampling}
|
||||
%! @sp 1
|
||||
%! Smooth Resampling of the particles (multivariate version).
|
||||
%! @sp 2
|
||||
%! @strong{Inputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item weights
|
||||
%! n*1 vector of doubles, particles' weights.
|
||||
%! @item particles
|
||||
%! n*1 vector of doubles, particles.
|
||||
%! @item number_of_new_particles
|
||||
%! Integer scalar.
|
||||
%! @item number_of_partitions
|
||||
%! Integer scalar.
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{Outputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item indx
|
||||
%! number_of_new_particles*1 vector of doubles, new particles.
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{This function is called by:}
|
||||
%! @sp 1
|
||||
%! @ref{particle/sequantial_importance_particle_filter}
|
||||
%! @sp 2
|
||||
%! @strong{This function calls:}
|
||||
%! @sp 1
|
||||
%! @ref{particle/univariate_smooth_resampling}
|
||||
%! @sp 2
|
||||
%! @end deftypefn
|
||||
%@eod:
|
||||
|
||||
% Copyright (C) 2012-2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
% AUTHOR(S) frederic DOT karame AT univ DASH lemans DOT fr
|
||||
% stephane DOT adjemian AT univ DASH lemans DOT fr
|
||||
|
||||
number_of_particles = length(weights);
|
||||
number_of_states = size(particles,2);
|
||||
[P,D] = eig(particles'*(bsxfun(@times,1/number_of_particles,particles))) ;
|
||||
D = diag(D) ;
|
||||
vectors = bsxfun(@times,P,sqrt(D)') ;
|
||||
orthogonalized_particles = bsxfun(@rdivide,particles*vectors,D') ;
|
||||
new_particles = zeros(number_of_particles,number_of_states) ;
|
||||
for j=1:number_of_states
|
||||
tout = sortrows( [orthogonalized_particles(:,j) weights],1) ;
|
||||
new_particles(:,j) = univariate_smooth_resampling(tout(:,2),tout(:,1),number_of_particles) ;
|
||||
end
|
||||
new_particles = new_particles*(vectors') ;
|
||||
|
|
@ -1,53 +0,0 @@
|
|||
function [c,SqrtVariance,Weights] = mykmeans(x,g,init,cod)
|
||||
|
||||
% Copyright (C) 2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
[n,m] = size(x) ;
|
||||
indold = zeros(1,m) ;
|
||||
if cod==0
|
||||
d = transpose(sum(bsxfun(@power,bsxfun(@minus,x,mean(x)),2)));
|
||||
d = sortrows( [transpose(1:m) d],2) ;
|
||||
d = d((1+(0:1:g-1))*m/g,1) ;
|
||||
c = x(:,d);
|
||||
else
|
||||
c = init ;
|
||||
end
|
||||
for iter=1:300
|
||||
dist = zeros(g,m) ;
|
||||
for i=1:g
|
||||
dist(i,:) = sum(bsxfun(@power,bsxfun(@minus,x,c(:,i)),2));
|
||||
end
|
||||
[rien,ind] = min(dist) ;
|
||||
if isequal(ind,indold)
|
||||
break ;
|
||||
end
|
||||
indold = ind ;
|
||||
for i=1:g
|
||||
lin = bsxfun(@eq,ind,i.*ones(1,m)) ;
|
||||
h = x(:,lin) ;
|
||||
c(:,i) = mean(h,2) ;
|
||||
end
|
||||
end
|
||||
SqrtVariance = zeros(n,n,g) ;
|
||||
Weights = zeros(1,g) ;
|
||||
for i=1:g
|
||||
temp = x(:,bsxfun(@eq,ind,i*ones(1,m))) ;
|
||||
u = bsxfun(@minus,temp,mean(temp,2)); %temp-mean(temp,1)' ;
|
||||
SqrtVariance(:,:,i) = chol( (u*u')/size(temp,2) )' ;
|
||||
Weights(i) = size(temp,2)/m ;
|
||||
end
|
||||
|
|
@ -1,21 +0,0 @@
|
|||
function n = neff(w)
|
||||
% Evaluates the criterion for resampling
|
||||
|
||||
% Copyright (C) 2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
n = dot(w,w);
|
||||
|
|
@ -1,373 +0,0 @@
|
|||
function [xparam,std_param,lb_95,ub_95,median_param] = online_auxiliary_filter(xparam1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults)
|
||||
|
||||
% Carvalho & Lopes particle filter = auxiliary particle filter including Liu & West filter on parameters.
|
||||
%
|
||||
% INPUTS
|
||||
% ReducedForm [structure] Matlab's structure describing the reduced form model.
|
||||
% ReducedForm.measurement.H [double] (pp x pp) variance matrix of measurement errors.
|
||||
% ReducedForm.state.Q [double] (qq x qq) variance matrix of state errors.
|
||||
% ReducedForm.state.dr [structure] output of resol.m.
|
||||
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
|
||||
% start [integer] scalar, likelihood evaluation starts at 'start'.
|
||||
% mf [integer] pp*1 vector of indices.
|
||||
% number_of_particles [integer] scalar.
|
||||
%
|
||||
% OUTPUTS
|
||||
% LIK [double] scalar, likelihood
|
||||
% lik [double] vector, density of observations in each period.
|
||||
%
|
||||
% REFERENCES
|
||||
%
|
||||
% NOTES
|
||||
% The vector "lik" is used to evaluate the jacobian of the likelihood.
|
||||
|
||||
% Copyright (C) 2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
persistent Y init_flag mf0 mf1 bounds number_of_particles number_of_parameters liu_west_delta liu_west_chol_sigma_bar
|
||||
persistent start_param sample_size number_of_observed_variables number_of_structural_innovations
|
||||
|
||||
% Set seed for randn().
|
||||
set_dynare_seed('default') ;
|
||||
pruning = DynareOptions.particle.pruning;
|
||||
second_resample = 1 ;
|
||||
variance_update = 1 ;
|
||||
|
||||
% initialization of state particles
|
||||
[ys,trend_coeff,exit_flag,info,Model,DynareOptions,BayesInfo,DynareResults,ReducedForm] = ...
|
||||
solve_model_for_online_filter(1,xparam1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults) ;
|
||||
|
||||
% Set persistent variables.
|
||||
if isempty(init_flag)
|
||||
mf0 = ReducedForm.mf0;
|
||||
mf1 = ReducedForm.mf1;
|
||||
number_of_particles = DynareOptions.particle.number_of_particles;
|
||||
number_of_parameters = size(xparam1,1) ;
|
||||
Y = DynareDataset.data ;
|
||||
sample_size = size(Y,2);
|
||||
number_of_observed_variables = length(mf1);
|
||||
number_of_structural_innovations = length(ReducedForm.Q);
|
||||
liu_west_delta = DynareOptions.particle.liu_west_delta ;
|
||||
%liu_west_chol_sigma_bar = DynareOptions.particle.liu_west_chol_sigma_bar*eye(number_of_parameters) ;
|
||||
start_param = xparam1 ;
|
||||
%liu_west_chol_sigma_bar = sqrt(bsxfun(@times,eye(number_of_parameters),BayesInfo.p2)) ;
|
||||
%start_param = BayesInfo.p1 ;
|
||||
bounds = [BayesInfo.lb BayesInfo.ub] ;
|
||||
init_flag = 1;
|
||||
end
|
||||
|
||||
% Get initial conditions for the state particles
|
||||
StateVectorMean = ReducedForm.StateVectorMean;
|
||||
StateVectorVarianceSquareRoot = reduced_rank_cholesky(ReducedForm.StateVectorVariance)';
|
||||
state_variance_rank = size(StateVectorVarianceSquareRoot,2);
|
||||
StateVectors = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean);
|
||||
if pruning
|
||||
StateVectors_ = StateVectors;
|
||||
end
|
||||
|
||||
% parameters for the Liu & West filter
|
||||
h_square = (3*liu_west_delta-1)/(2*liu_west_delta) ;
|
||||
h_square = 1-h_square*h_square ;
|
||||
small_a = sqrt(1-h_square) ;
|
||||
|
||||
% Initialization of parameter particles
|
||||
xparam = zeros(number_of_parameters,number_of_particles) ;
|
||||
stderr = sqrt(bsxfun(@power,bounds(:,2)+bounds(:,1),2)/12)/100 ;
|
||||
stderr = sqrt(bsxfun(@power,bounds(:,2)+bounds(:,1),2)/12)/50 ;
|
||||
i = 1 ;
|
||||
while i<=number_of_particles
|
||||
%candidate = start_param + .001*liu_west_chol_sigma_bar*randn(number_of_parameters,1) ;
|
||||
candidate = start_param + bsxfun(@times,stderr,randn(number_of_parameters,1)) ;
|
||||
if all(candidate(:) >= bounds(:,1)) && all(candidate(:) <= bounds(:,2))
|
||||
xparam(:,i) = candidate(:) ;
|
||||
i = i+1 ;
|
||||
end
|
||||
end
|
||||
|
||||
%xparam = bsxfun(@plus,bounds(:,1),bsxfun(@times,(bounds(:,2)-bounds(:,1)),rand(number_of_parameters,number_of_particles))) ;
|
||||
|
||||
% Initialization of the weights of particles.
|
||||
weights = ones(1,number_of_particles)/number_of_particles ;
|
||||
|
||||
% Initialization of the likelihood.
|
||||
const_lik = log(2*pi)*number_of_observed_variables;
|
||||
mean_xparam = zeros(number_of_parameters,sample_size) ;
|
||||
median_xparam = zeros(number_of_parameters,sample_size) ;
|
||||
std_xparam = zeros(number_of_parameters,sample_size) ;
|
||||
lb95_xparam = zeros(number_of_parameters,sample_size) ;
|
||||
ub95_xparam = zeros(number_of_parameters,sample_size) ;
|
||||
|
||||
%% The Online filter
|
||||
for t=1:sample_size
|
||||
disp(t)
|
||||
% Moments of parameters particles distribution
|
||||
m_bar = xparam*(weights') ;
|
||||
temp = bsxfun(@minus,xparam,m_bar) ;
|
||||
sigma_bar = (bsxfun(@times,weights,temp))*(temp') ;
|
||||
if variance_update==1
|
||||
chol_sigma_bar = chol(h_square*sigma_bar)' ;
|
||||
end
|
||||
% Prediction (without shocks)
|
||||
ObservedVariables = zeros(number_of_observed_variables,number_of_particles) ;
|
||||
for i=1:number_of_particles
|
||||
% model resolution
|
||||
[ys,trend_coeff,exit_flag,info,Model,DynareOptions,BayesInfo,DynareResults,ReducedForm] = ...
|
||||
solve_model_for_online_filter(t,xparam(:,i),DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults) ;
|
||||
steadystate = ReducedForm.steadystate;
|
||||
state_variables_steady_state = ReducedForm.state_variables_steady_state;
|
||||
% Set local state space model (second-order approximation).
|
||||
constant = ReducedForm.constant;
|
||||
ghx = ReducedForm.ghx;
|
||||
ghu = ReducedForm.ghu;
|
||||
ghxx = ReducedForm.ghxx;
|
||||
ghuu = ReducedForm.ghuu;
|
||||
ghxu = ReducedForm.ghxu;
|
||||
% particle likelihood contribution
|
||||
yhat = bsxfun(@minus,StateVectors(:,i),state_variables_steady_state);
|
||||
if pruning
|
||||
yhat_ = bsxfun(@minus,StateVectors_(:,i),state_variables_steady_state);
|
||||
[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);
|
||||
else
|
||||
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);
|
||||
end
|
||||
ObservedVariables(:,i) = tmp(mf1,:) ;
|
||||
end
|
||||
PredictedObservedMean = sum(bsxfun(@times,weights,ObservedVariables),2) ;
|
||||
PredictionError = bsxfun(@minus,Y(:,t),ObservedVariables);
|
||||
dPredictedObservedMean = bsxfun(@minus,ObservedVariables,PredictedObservedMean);
|
||||
PredictedObservedVariance = bsxfun(@times,weights,dPredictedObservedMean)*dPredictedObservedMean' + ReducedForm.H ;
|
||||
wtilde = exp(-.5*(const_lik+log(det(PredictedObservedVariance))+sum(PredictionError.*(PredictedObservedVariance\PredictionError),1))) ;
|
||||
% unormalized weights and observation likelihood contribution
|
||||
tau_tilde = weights.*wtilde ;
|
||||
sum_tau_tilde = sum(tau_tilde) ;
|
||||
% particles selection
|
||||
tau_tilde = tau_tilde/sum_tau_tilde ;
|
||||
indx = index_resample(0,tau_tilde',DynareOptions);
|
||||
StateVectors = StateVectors(:,indx) ;
|
||||
if pruning
|
||||
StateVectors_ = StateVectors_(:,indx) ;
|
||||
end
|
||||
xparam = bsxfun(@plus,(1-small_a).*m_bar,small_a.*xparam) ;
|
||||
xparam = xparam(:,indx) ;
|
||||
wtilde = wtilde(indx) ;
|
||||
% draw in the new distributions
|
||||
i = 1 ;
|
||||
while i<=number_of_particles
|
||||
candidate = xparam(:,i) + chol_sigma_bar*randn(number_of_parameters,1) ;
|
||||
if all(candidate >= bounds(:,1)) && all(candidate <= bounds(:,2))
|
||||
xparam(:,i) = candidate ;
|
||||
% model resolution for new parameters particles
|
||||
[ys,trend_coeff,exit_flag,info,Model,DynareOptions,BayesInfo,DynareResults,ReducedForm] = ...
|
||||
solve_model_for_online_filter(t,xparam(:,i),DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults) ;
|
||||
steadystate = ReducedForm.steadystate;
|
||||
state_variables_steady_state = ReducedForm.state_variables_steady_state;
|
||||
% Set local state space model (second order approximation).
|
||||
constant = ReducedForm.constant;
|
||||
ghx = ReducedForm.ghx;
|
||||
ghu = ReducedForm.ghu;
|
||||
ghxx = ReducedForm.ghxx;
|
||||
ghuu = ReducedForm.ghuu;
|
||||
ghxu = ReducedForm.ghxu;
|
||||
% Get covariance matrices and structural shocks
|
||||
epsilon = chol(ReducedForm.Q)'*randn(number_of_structural_innovations,1) ;
|
||||
% compute particles likelihood contribution
|
||||
yhat = bsxfun(@minus,StateVectors(:,i),state_variables_steady_state);
|
||||
if pruning
|
||||
yhat_ = bsxfun(@minus,StateVectors_(:,i),state_variables_steady_state);
|
||||
[tmp, tmp_] = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,DynareOptions.threads.local_state_space_iteration_2);
|
||||
StateVectors_(:,i) = tmp_(mf0,:) ;
|
||||
else
|
||||
tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
|
||||
end
|
||||
StateVectors(:,i) = tmp(mf0,:) ;
|
||||
ObservedVariables(:,i) = tmp(mf1,:) ;
|
||||
i = i+1 ;
|
||||
end
|
||||
end
|
||||
PredictedObservedMean = sum(bsxfun(@times,weights,ObservedVariables),2) ;
|
||||
PredictionError = bsxfun(@minus,Y(:,t),ObservedVariables);
|
||||
dPredictedObservedMean = bsxfun(@minus,ObservedVariables,PredictedObservedMean);
|
||||
PredictedObservedVariance = bsxfun(@times,weights,dPredictedObservedMean)*dPredictedObservedMean' + ReducedForm.H ;
|
||||
lnw = exp(-.5*(const_lik+log(det(PredictedObservedVariance))+sum(PredictionError.*(PredictedObservedVariance\PredictionError),1)));
|
||||
% importance ratio
|
||||
wtilde = lnw./wtilde ;
|
||||
% normalization
|
||||
weights = wtilde/sum(wtilde);
|
||||
if (variance_update==1) && (neff(weights)<DynareOptions.particle.resampling.threshold*sample_size)
|
||||
variance_update = 0 ;
|
||||
end
|
||||
% final resampling (advised)
|
||||
if second_resample==1
|
||||
indx = index_resample(0,weights,DynareOptions);
|
||||
StateVectors = StateVectors(:,indx) ;
|
||||
if pruning
|
||||
StateVectors_ = StateVectors_(:,indx) ;
|
||||
end
|
||||
xparam = xparam(:,indx) ;
|
||||
weights = ones(1,number_of_particles)/number_of_particles ;
|
||||
mean_xparam(:,t) = mean(xparam,2);
|
||||
mat_var_cov = bsxfun(@minus,xparam,mean_xparam(:,t)) ;
|
||||
mat_var_cov = (mat_var_cov*mat_var_cov')/(number_of_particles-1) ;
|
||||
std_xparam(:,t) = sqrt(diag(mat_var_cov)) ;
|
||||
for i=1:number_of_parameters
|
||||
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)) ;
|
||||
for i=1:number_of_parameters
|
||||
temp = sortrows([xparam(i,:)' weights'],1) ;
|
||||
cumulated_weights = cumsum(temp(:,2)) ;
|
||||
pass1=1 ;
|
||||
pass2=1 ;
|
||||
pass3=1 ;
|
||||
for j=1:number_of_particles
|
||||
if cumulated_weights(j)>0.025 && pass1==1
|
||||
lb95_xparam(i,t) = (temp(j-1,1)+temp(j,1))/2 ;
|
||||
pass1 = 2 ;
|
||||
end
|
||||
if cumulated_weights(j)>0.5 && pass2==1
|
||||
median_xparam(i,t) = (temp(j-1,1)+temp(j,1))/2 ;
|
||||
pass2 = 2 ;
|
||||
end
|
||||
if cumulated_weights(j)>0.975 && pass3==1
|
||||
ub95_xparam(i,t) = (temp(j-1,1)+temp(j,1))/2 ;
|
||||
pass3 = 2 ;
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
disp([lb95_xparam(:,t) mean_xparam(:,t) ub95_xparam(:,t)])
|
||||
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) ;
|
||||
|
||||
%% Plot parameters trajectory
|
||||
TeX = DynareOptions.TeX;
|
||||
|
||||
[nbplt,nr,nc,lr,lc,nstar] = pltorg(number_of_parameters);
|
||||
|
||||
if TeX
|
||||
fidTeX = fopen([Model.fname '_param_traj.TeX'],'w');
|
||||
fprintf(fidTeX,'%% TeX eps-loader file generated by online_auxiliary_filter.m (Dynare).\n');
|
||||
fprintf(fidTeX,['%% ' datestr(now,0) '\n']);
|
||||
fprintf(fidTeX,' \n');
|
||||
end
|
||||
|
||||
z = 1:1:sample_size ;
|
||||
|
||||
for plt = 1:nbplt,
|
||||
if TeX
|
||||
NAMES = [];
|
||||
TeXNAMES = [];
|
||||
end
|
||||
hh = dyn_figure(DynareOptions,'Name','Parameters Trajectories');
|
||||
for k=1:min(nstar,length(xparam)-(plt-1)*nstar)
|
||||
subplot(nr,nc,k)
|
||||
kk = (plt-1)*nstar+k;
|
||||
[name,texname] = get_the_name(kk,TeX,Model,EstimatedParameters,DynareOptions);
|
||||
if TeX
|
||||
if isempty(NAMES)
|
||||
NAMES = name;
|
||||
TeXNAMES = texname;
|
||||
else
|
||||
NAMES = char(NAMES,name);
|
||||
TeXNAMES = char(TeXNAMES,texname);
|
||||
end
|
||||
end
|
||||
y = [mean_xparam(kk,:)' median_xparam(kk,:)' lb95_xparam(kk,:)' ub95_xparam(kk,:)' xparam(kk)*ones(sample_size,1)] ;
|
||||
plot(z,y);
|
||||
hold on
|
||||
title(name,'interpreter','none')
|
||||
hold off
|
||||
axis tight
|
||||
drawnow
|
||||
end
|
||||
dyn_saveas(hh,[ Model.fname '_param_traj' int2str(plt) ],DynareOptions);
|
||||
if TeX
|
||||
% TeX eps loader file
|
||||
fprintf(fidTeX,'\\begin{figure}[H]\n');
|
||||
for jj = 1:min(nstar,length(x)-(plt-1)*nstar)
|
||||
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_ParamTraj%s}\n',Model.fname,int2str(plt));
|
||||
fprintf(fidTeX,'\\caption{Parameters trajectories.}');
|
||||
fprintf(fidTeX,'\\label{Fig:ParametersPlots:%s}\n',int2str(plt));
|
||||
fprintf(fidTeX,'\\end{figure}\n');
|
||||
fprintf(fidTeX,' \n');
|
||||
end
|
||||
end
|
||||
|
||||
%% 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,
|
||||
if TeX
|
||||
NAMES = [];
|
||||
TeXNAMES = [];
|
||||
end
|
||||
hh = dyn_figure(DynareOptions,'Name','Parameters Densities');
|
||||
for k=1:min(nstar,length(xparam)-(plt-1)*nstar)
|
||||
subplot(nr,nc,k)
|
||||
kk = (plt-1)*nstar+k;
|
||||
[name,texname] = get_the_name(kk,TeX,Model,EstimatedParameters,DynareOptions);
|
||||
if TeX
|
||||
if isempty(NAMES)
|
||||
NAMES = name;
|
||||
TeXNAMES = texname;
|
||||
else
|
||||
NAMES = char(NAMES,name);
|
||||
TeXNAMES = char(TeXNAMES,texname);
|
||||
end
|
||||
end
|
||||
optimal_bandwidth = mh_optimal_bandwidth(distrib_param(kk,:)',number_of_particles,bandwidth,kernel_function);
|
||||
[density(:,1),density(:,2)] = kernel_density_estimate(distrib_param(kk,:)',number_of_grid_points,...
|
||||
number_of_particles,optimal_bandwidth,kernel_function);
|
||||
plot(density(:,1),density(:,2));
|
||||
hold on
|
||||
title(name,'interpreter','none')
|
||||
hold off
|
||||
axis tight
|
||||
drawnow
|
||||
end
|
||||
dyn_saveas(hh,[ Model.fname '_param_density' int2str(plt) ],DynareOptions);
|
||||
if TeX
|
||||
% TeX eps loader file
|
||||
fprintf(fidTeX,'\\begin{figure}[H]\n');
|
||||
for jj = 1:min(nstar,length(x)-(plt-1)*nstar)
|
||||
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));
|
||||
fprintf(fidTeX,'\\caption{ParametersDensities.}');
|
||||
fprintf(fidTeX,'\\label{Fig:ParametersDensities:%s}\n',int2str(plt));
|
||||
fprintf(fidTeX,'\\end{figure}\n');
|
||||
fprintf(fidTeX,' \n');
|
||||
end
|
||||
end
|
||||
|
||||
|
|
@ -1,39 +0,0 @@
|
|||
function [prior,likelihood,C,posterior] = probability(mu,sqrtP,prior,X)
|
||||
|
||||
% Copyright (C) 2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
[dim,nov] = size(X);
|
||||
M = size(mu,2) ;
|
||||
if nargout>1
|
||||
likelihood = zeros(M,nov);
|
||||
normfact = (2*pi)^(dim/2);
|
||||
for k=1:M
|
||||
XX = bsxfun(@minus,X,mu(:,k));
|
||||
S = sqrtP(:,:,k);
|
||||
foo = S \ XX;
|
||||
likelihood(k,:) = exp(-0.5*sum(foo.*foo, 1))/abs((normfact*prod(diag(S))));
|
||||
end
|
||||
end
|
||||
likelihood = likelihood + 1e-99;
|
||||
if nargout>2
|
||||
C = prior*likelihood + 1e-99;
|
||||
end
|
||||
if nargout>3
|
||||
posterior = bsxfun(@rdivide,bsxfun(@times,prior',likelihood),C) + 1e-99 ;
|
||||
posterior = bsxfun(@rdivide,posterior,sum(posterior,1));
|
||||
end
|
||||
|
|
@ -1,38 +0,0 @@
|
|||
function [density] = probability2(mu,S,X)
|
||||
%
|
||||
% Multivariate gaussian density
|
||||
%
|
||||
% INPUTS
|
||||
% n [integer] scalar, number of variables.
|
||||
%
|
||||
% OUTPUTS
|
||||
% nodes [double] nodes of the cubature
|
||||
% weigths [double] associated weigths
|
||||
%
|
||||
% REFERENCES
|
||||
%
|
||||
%
|
||||
% NOTES
|
||||
%
|
||||
% Copyright (C) 2009-2012 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
dim = size(X,1) ;
|
||||
normfact = bsxfun(@power,(2*pi),(dim/2)) ;
|
||||
foo = S\(bsxfun(@minus,X,mu)) ;
|
||||
density = exp(-0.5*sum(foo.*foo)')./abs((normfact*prod(diag(S)))) + 1e-99 ;
|
||||
|
||||
|
|
@ -1,74 +0,0 @@
|
|||
function resampled_particles = resample(particles,weights,DynareOptions)
|
||||
% Resamples particles.
|
||||
|
||||
%@info:
|
||||
%! @deftypefn {Function File} {@var{indx} =} resample (@var{weights}, @var{method})
|
||||
%! @anchor{particle/resample}
|
||||
%! @sp 1
|
||||
%! Resamples particles.
|
||||
%! @sp 2
|
||||
%! @strong{Inputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item weights
|
||||
%! n*1 vector of doubles, particles' weights.
|
||||
%! @item method
|
||||
%! string equal to 'residual' or 'traditional'.
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{Outputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item indx
|
||||
%! n*1 vector of intergers, indices.
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{This function is called by:}
|
||||
%! @sp 1
|
||||
%! @ref{particle/sequantial_importance_particle_filter}
|
||||
%! @sp 2
|
||||
%! @strong{This function calls:}
|
||||
%! @sp 1
|
||||
%! @ref{residual_resampling}, @ref{traditional_resampling}
|
||||
%! @sp 2
|
||||
%! @end deftypefn
|
||||
%@eod:
|
||||
|
||||
% Copyright (C) 2011-2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
defaultmethod = 1; % For residual based method set this variable equal to 0.
|
||||
|
||||
if defaultmethod
|
||||
if DynareOptions.particle.resampling.method.kitagawa
|
||||
resampled_particles = traditional_resampling(particles,weights,rand);
|
||||
elseif DynareOptions.particle.resampling.method.stratified
|
||||
resampled_particles = traditional_resampling(particles,weights,rand(size(weights)));
|
||||
elseif DynareOptions.particle.resampling.method.smooth
|
||||
resampled_particles = multivariate_smooth_resampling(particles,weights);
|
||||
else
|
||||
error('Unknow sampling method!')
|
||||
end
|
||||
else
|
||||
if DynareOptions.particle.resampling.method.kitagawa
|
||||
resampled_particles = residual_resampling(particles,weights,rand);
|
||||
elseif DynareOptions.particle.resampling.method.stratified
|
||||
resampled_particles = residual_resampling(particles,weights,rand(size(weights)));
|
||||
else
|
||||
error('Unknown sampling method!')
|
||||
end
|
||||
end
|
||||
|
|
@ -1,143 +0,0 @@
|
|||
function return_resample = residual_resampling(particles,weights,noise)
|
||||
% Resamples particles.
|
||||
|
||||
%@info:
|
||||
%! @deftypefn {Function File} {@var{indx} =} residual_resampling (@var{weights})
|
||||
%! @anchor{particle/residual_resampling}
|
||||
%! @sp 1
|
||||
%! Resamples particles.
|
||||
%! @sp 2
|
||||
%! @strong{Inputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item weights
|
||||
%! n*1 vector of doubles, particles' weights.
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{Outputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item indx
|
||||
%! n*1 vector of intergers, indices.
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{This function is called by:}
|
||||
%! @sp 1
|
||||
%! @ref{particle/resample}
|
||||
%! @sp 2
|
||||
%! @strong{This function calls:}
|
||||
%! @sp 2
|
||||
%! @end deftypefn
|
||||
%@eod:
|
||||
|
||||
% Copyright (C) 2011-2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
% AUTHOR(S) frederic DOT karame AT univ DASH evry DOT fr
|
||||
% stephane DOT adjemian AT univ DASH lemans DOT fr
|
||||
|
||||
% What is the number of particles?
|
||||
number_of_particles = length(weights);
|
||||
|
||||
switch length(noise)
|
||||
case 1
|
||||
kitagawa_resampling = 1;
|
||||
case number_of_particles
|
||||
kitagawa_resampling = 0;
|
||||
otherwise
|
||||
error(['particle::resampling: Unknown method! The size of the second argument (' inputname(3) ') is wrong.'])
|
||||
end
|
||||
|
||||
% Set vectors of indices.
|
||||
jndx = 1:number_of_particles;
|
||||
indx = zeros(1,number_of_particles);
|
||||
|
||||
% Multiply the weights by the number of particles.
|
||||
WEIGHTS = number_of_particles*weights;
|
||||
|
||||
% Compute the integer part of the normalized weights.
|
||||
iWEIGHTS = fix(WEIGHTS);
|
||||
|
||||
% Compute the number of resample
|
||||
number_of_trials = number_of_particles-sum(iWEIGHTS);
|
||||
|
||||
if number_of_trials
|
||||
WEIGHTS = (WEIGHTS-iWEIGHTS)/number_of_trials;
|
||||
EmpiricalCDF = cumsum(WEIGHTS);
|
||||
if kitagawa_resampling
|
||||
u = (transpose(1:number_of_trials)-1+noise(:))/number_of_trials;
|
||||
else
|
||||
u = fliplr(cumprod(noise(1:number_of_trials).^(1./(number_of_trials:-1:1))));
|
||||
end
|
||||
j=1;
|
||||
for i=1:number_of_trials
|
||||
while (u(i)>EmpiricalCDF(j))
|
||||
j=j+1;
|
||||
end
|
||||
iWEIGHTS(j)=iWEIGHTS(j)+1;
|
||||
if kitagawa_resampling==0
|
||||
j=1;
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
k=1;
|
||||
for i=1:number_of_particles
|
||||
if (iWEIGHTS(i)>0)
|
||||
for j=k:k+iWEIGHTS(i)-1
|
||||
indx(j) = jndx(i);
|
||||
end
|
||||
end
|
||||
k = k + iWEIGHTS(i);
|
||||
end
|
||||
|
||||
if particles==0
|
||||
return_resample = indx ;
|
||||
else
|
||||
return_resample = particles(indx,:) ;
|
||||
end
|
||||
%@test:1
|
||||
%$ % Define the weights
|
||||
%$ weights = randn(2000,1).^2;
|
||||
%$ weights = weights/sum(weights);
|
||||
%$ % Initialize t.
|
||||
%$ t = ones(1,1);
|
||||
%$
|
||||
%$ try
|
||||
%$ indx1 = residual_resampling(weights);
|
||||
%$ catch
|
||||
%$ t(1) = 0;
|
||||
%$ end
|
||||
%$
|
||||
%$ T = all(t);
|
||||
%@eof:1
|
||||
|
||||
%@test:2
|
||||
%$ % Define the weights
|
||||
%$ weights = exp(randn(2000,1));
|
||||
%$ weights = weights/sum(weights);
|
||||
%$ % Initialize t.
|
||||
%$ t = ones(1,1);
|
||||
%$
|
||||
%$ try
|
||||
%$ indx1 = residual_resampling(weights);
|
||||
%$ catch
|
||||
%$ t(1) = 0;
|
||||
%$ end
|
||||
%$
|
||||
%$ T = all(t);
|
||||
%@eof:2
|
||||
|
|
@ -1,178 +0,0 @@
|
|||
function [LIK,lik] = sequential_importance_particle_filter(ReducedForm,Y,start,DynareOptions)
|
||||
% Evaluates the likelihood of a nonlinear model with a particle filter (optionally with resampling).
|
||||
% Standard Sequential Monte Carlo approach with
|
||||
% - the usual proposal (the state transition distribution)
|
||||
% - options on resampling: none, adaptive or systematic
|
||||
%@info:
|
||||
%! @deftypefn {Function File} {@var{y}, @var{y_} =} sequential_importance_particle_filter (@var{ReducedForm},@var{Y}, @var{start}, @var{DynareOptions})
|
||||
%! @anchor{particle/sequential_importance_particle_filter}
|
||||
%! @sp 1
|
||||
%! Evaluates the likelihood of a nonlinear model with a particle filter (optionally with resampling).
|
||||
%!
|
||||
%! @sp 2
|
||||
%! @strong{Inputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item ReducedForm
|
||||
%! Structure describing the state space model (built in @ref{non_linear_dsge_likelihood}).
|
||||
%! @item Y
|
||||
%! p*smpl matrix of doubles (p is the number of observed variables), the (detrended) data.
|
||||
%! @item start
|
||||
%! Integer scalar, likelihood evaluation starts at observation 'start'.
|
||||
%! @item DynareOptions
|
||||
%! Structure specifying Dynare's options.
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{Outputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item LIK
|
||||
%! double scalar, value of (minus) the logged likelihood.
|
||||
%! @item lik
|
||||
%! smpl*1 vector of doubles, density of the observations at each period.
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{This function is called by:}
|
||||
%! @ref{non_linear_dsge_likelihood}
|
||||
%! @sp 2
|
||||
%! @strong{This function calls:}
|
||||
%!
|
||||
%! @end deftypefn
|
||||
%@eod:
|
||||
|
||||
% Copyright (C) 2011-2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
% AUTHOR(S) frederic DOT karame AT univ DASH lemans DOT fr
|
||||
% stephane DOT adjemian AT univ DASH lemans DOT fr
|
||||
|
||||
persistent init_flag
|
||||
persistent mf0 mf1
|
||||
persistent number_of_particles number_of_state_variables
|
||||
persistent sample_size number_of_observed_variables number_of_structural_innovations
|
||||
|
||||
% Set default value for start
|
||||
if isempty(start)
|
||||
start = 1;
|
||||
end
|
||||
|
||||
% Set flag for prunning
|
||||
pruning = DynareOptions.particle.pruning;
|
||||
|
||||
% Get steady state and mean.
|
||||
steadystate = ReducedForm.steadystate;
|
||||
constant = ReducedForm.constant;
|
||||
state_variables_steady_state = ReducedForm.state_variables_steady_state;
|
||||
|
||||
% Set persistent variables (if needed).
|
||||
if isempty(init_flag)
|
||||
mf0 = ReducedForm.mf0;
|
||||
mf1 = ReducedForm.mf1;
|
||||
sample_size = size(Y,2);
|
||||
number_of_state_variables = length(mf0);
|
||||
number_of_observed_variables = length(mf1);
|
||||
number_of_structural_innovations = length(ReducedForm.Q);
|
||||
number_of_particles = DynareOptions.particle.number_of_particles;
|
||||
init_flag = 1;
|
||||
end
|
||||
|
||||
% Set local state space model (first order approximation).
|
||||
ghx = ReducedForm.ghx;
|
||||
ghu = ReducedForm.ghu;
|
||||
|
||||
% Set local state space model (second order approximation).
|
||||
ghxx = ReducedForm.ghxx;
|
||||
ghuu = ReducedForm.ghuu;
|
||||
ghxu = ReducedForm.ghxu;
|
||||
|
||||
% Get covariance matrices.
|
||||
Q = ReducedForm.Q; % Covariance matrix of the structural innovations.
|
||||
H = ReducedForm.H; % Covariance matrix of the measurement errors.
|
||||
if isempty(H)
|
||||
H = 0;
|
||||
end
|
||||
|
||||
% Initialization of the likelihood.
|
||||
const_lik = log(2*pi)*number_of_observed_variables;
|
||||
lik = NaN(sample_size,1);
|
||||
|
||||
% Get initial condition for the state vector.
|
||||
StateVectorMean = ReducedForm.StateVectorMean;
|
||||
StateVectorVarianceSquareRoot = reduced_rank_cholesky(ReducedForm.StateVectorVariance)';
|
||||
if pruning
|
||||
StateVectorMean_ = StateVectorMean;
|
||||
StateVectorVarianceSquareRoot_ = StateVectorVarianceSquareRoot;
|
||||
end
|
||||
|
||||
% Get the rank of StateVectorVarianceSquareRoot
|
||||
state_variance_rank = size(StateVectorVarianceSquareRoot,2);
|
||||
|
||||
% Factorize the covariance matrix of the structural innovations
|
||||
Q_lower_triangular_cholesky = chol(Q)';
|
||||
|
||||
% Set seed for randn().
|
||||
set_dynare_seed('default');
|
||||
|
||||
% Initialization of the weights across particles.
|
||||
weights = ones(1,number_of_particles)/number_of_particles ;
|
||||
StateVectors = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean);
|
||||
if pruning
|
||||
StateVectors_ = StateVectors;
|
||||
end
|
||||
|
||||
% Loop over observations
|
||||
for t=1:sample_size
|
||||
yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
|
||||
epsilon = Q_lower_triangular_cholesky*randn(number_of_structural_innovations,number_of_particles);
|
||||
if pruning
|
||||
yhat_ = bsxfun(@minus,StateVectors_,state_variables_steady_state);
|
||||
[tmp, tmp_] = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,DynareOptions.threads.local_state_space_iteration_2);
|
||||
else
|
||||
tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
|
||||
end
|
||||
PredictedObservedMean = tmp(mf1,:)*transpose(weights);
|
||||
PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:));
|
||||
dPredictedObservedMean = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean);
|
||||
PredictedObservedVariance = bsxfun(@times,dPredictedObservedMean,weights)*dPredictedObservedMean' + H;
|
||||
if rcond(PredictedObservedVariance) > 1e-16
|
||||
lnw = -.5*(const_lik+log(det(PredictedObservedVariance))+sum(PredictionError.*(PredictedObservedVariance\PredictionError),1));
|
||||
else
|
||||
LIK = NaN;
|
||||
return
|
||||
end
|
||||
dfac = max(lnw);
|
||||
wtilde = weights.*exp(lnw-dfac);
|
||||
lik(t) = log(sum(wtilde))+dfac;
|
||||
weights = wtilde/sum(wtilde);
|
||||
if (DynareOptions.particle.resampling.status.generic && neff(weights)<DynareOptions.particle.resampling.threshold*sample_size) || DynareOptions.particle.resampling.status.systematic
|
||||
if pruning
|
||||
temp = resample([tmp(mf0,:)' tmp_(mf0,:)'],weights',DynareOptions);
|
||||
StateVectors = temp(:,1:number_of_state_variables)';
|
||||
StateVectors_ = temp(:,number_of_state_variables+1:2*number_of_state_variables)';
|
||||
else
|
||||
StateVectors = resample(tmp(mf0,:)',weights',DynareOptions)';
|
||||
end
|
||||
weights = ones(1,number_of_particles)/number_of_particles;
|
||||
elseif DynareOptions.particle.resampling.status.none
|
||||
StateVectors = tmp(mf0,:);
|
||||
if pruning
|
||||
StateVectors_ = tmp_(mf0,:);
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
LIK = -sum(lik(start:end));
|
||||
|
|
@ -1,344 +0,0 @@
|
|||
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.
|
||||
|
||||
%@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:
|
||||
|
||||
% Copyright (C) 2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
% AUTHOR(S) stephane DOT adjemian AT univ DASH lemans DOT fr
|
||||
% frederic DOT karame AT univ DASH lemans DOT fr
|
||||
|
||||
%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
|
||||
|
||||
% Initialization of the returned arguments.
|
||||
fval = [];
|
||||
ys = [];
|
||||
trend_coeff = [];
|
||||
exit_flag = 1;
|
||||
|
||||
% Set the number of observed variables
|
||||
nvobs = DynareDataset.info.nvobs;
|
||||
|
||||
%------------------------------------------------------------------------------
|
||||
% 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
|
||||
|
||||
% 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
|
||||
|
||||
% Get the diagonal elements of the covariance matrices for the structural innovations (Q) and the measurement error (H).
|
||||
Q = Model.Sigma_e;
|
||||
H = Model.H;
|
||||
for i=1:EstimatedParameters.nvx
|
||||
k =EstimatedParameters.var_exo(i,1);
|
||||
Q(k,k) = xparam1(i)*xparam1(i);
|
||||
end
|
||||
offset = EstimatedParameters.nvx;
|
||||
if EstimatedParameters.nvn
|
||||
for i=1:EstimatedParameters.nvn
|
||||
H(i,i) = xparam1(i+offset)*xparam1(i+offset);
|
||||
end
|
||||
offset = offset+EstimatedParameters.nvn;
|
||||
else
|
||||
H = zeros(nvobs);
|
||||
end
|
||||
|
||||
% Get the off-diagonal elements of the covariance matrix for the structural innovations. Test if Q is positive definite.
|
||||
if EstimatedParameters.ncx
|
||||
for i=1:EstimatedParameters.ncx
|
||||
k1 =EstimatedParameters.corrx(i,1);
|
||||
k2 =EstimatedParameters.corrx(i,2);
|
||||
Q(k1,k2) = xparam1(i+offset)*sqrt(Q(k1,k1)*Q(k2,k2));
|
||||
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
|
||||
offset = offset+EstimatedParameters.ncx;
|
||||
end
|
||||
|
||||
% Get the off-diagonal elements of the covariance matrix for the measurement errors. Test if H is positive definite.
|
||||
if EstimatedParameters.ncn
|
||||
corrn_observable_correspondence = EstimatedParameters.corrn_observable_correspondence;
|
||||
for i=1:EstimatedParameters.ncn
|
||||
k1 = corrn_observable_correspondence(i,1);
|
||||
k2 = corrn_observable_correspondence(i,2);
|
||||
H(k1,k2) = xparam1(i+offset)*sqrt(H(k1,k1)*H(k2,k2));
|
||||
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
|
||||
offset = offset+EstimatedParameters.ncn;
|
||||
end
|
||||
|
||||
% Update estimated structural parameters in Mode.params.
|
||||
if EstimatedParameters.np > 0
|
||||
Model.params(EstimatedParameters.param_vals(:,1)) = xparam1(offset+1:end);
|
||||
end
|
||||
|
||||
% Update Model.Sigma_e and Model.H.
|
||||
Model.Sigma_e = Q;
|
||||
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');
|
||||
|
||||
%if info(1) == 1 || info(1) == 2 || info(1) == 5
|
||||
% fval = objective_function_penalty_base+1;
|
||||
% exit_flag = 0;
|
||||
% return
|
||||
%elseif info(1) == 3 || info(1) == 4 || info(1)==6 ||info(1) == 19 || info(1) == 20 || info(1) == 21
|
||||
% fval = objective_function_penalty_base+info(2);
|
||||
% exit_flag = 0;
|
||||
% 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.rawdata);
|
||||
|
||||
%------------------------------------------------------------------------------
|
||||
% 3. Initial condition of the Kalman filter
|
||||
%------------------------------------------------------------------------------
|
||||
|
||||
% Get decision rules and transition equations.
|
||||
dr = DynareResults.dr;
|
||||
|
||||
% Set persistent variables (first call).
|
||||
if isempty(init_flag)
|
||||
mf0 = BayesInfo.mf0;
|
||||
mf1 = BayesInfo.mf1;
|
||||
restrict_variables_idx = BayesInfo.restrict_var_list;
|
||||
observed_variables_idx = restrict_variables_idx(mf1);
|
||||
state_variables_idx = restrict_variables_idx(mf0);
|
||||
sample_size = size(Y,2);
|
||||
number_of_state_variables = length(mf0);
|
||||
number_of_observed_variables = length(mf1);
|
||||
number_of_structural_innovations = length(Q);
|
||||
init_flag = 1;
|
||||
end
|
||||
|
||||
ReducedForm.ghx = dr.ghx(restrict_variables_idx,:);
|
||||
ReducedForm.ghu = dr.ghu(restrict_variables_idx,:);
|
||||
ReducedForm.ghxx = dr.ghxx(restrict_variables_idx,:);
|
||||
ReducedForm.ghuu = dr.ghuu(restrict_variables_idx,:);
|
||||
ReducedForm.ghxu = dr.ghxu(restrict_variables_idx,:);
|
||||
ReducedForm.steadystate = dr.ys(dr.order_var(restrict_variables_idx));
|
||||
ReducedForm.constant = ReducedForm.steadystate + .5*dr.ghs2(restrict_variables_idx);
|
||||
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
|
||||
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);
|
||||
StateVectorVariance = lyapunov_symm(ReducedForm.ghx(mf0,:),ReducedForm.ghu(mf0,:)*ReducedForm.Q*ReducedForm.ghu(mf0,:)',1e-12,1e-12,[],[],DynareOptions.debug);
|
||||
case 2% Initial state vector covariance is a monte-carlo based estimate of the ergodic variance (consistent with a k-order Taylor-approximation of the model).
|
||||
StateVectorMean = ReducedForm.constant(mf0);
|
||||
old_DynareOptionsperiods = DynareOptions.periods;
|
||||
DynareOptions.periods = 5000;
|
||||
y_ = simult(oo_.steady_state, dr,Model,DynareOptions,DynareResults);
|
||||
y_ = y_(state_variables_idx,2001:5000);
|
||||
StateVectorVariance = cov(y_');
|
||||
DynareOptions.periods = old_DynareOptionsperiods;
|
||||
clear('old_DynareOptionsperiods','y_');
|
||||
case 3% Initial state vector covariance is a diagonal matrix.
|
||||
StateVectorMean = ReducedForm.constant(mf0);
|
||||
StateVectorVariance = DynareOptions.particle.initial_state_prior_std*eye(number_of_state_variables);
|
||||
otherwise
|
||||
error('Unknown initialization option!')
|
||||
end
|
||||
ReducedForm.StateVectorMean = StateVectorMean;
|
||||
ReducedForm.StateVectorVariance = StateVectorVariance;
|
||||
end
|
||||
|
|
@ -1,36 +0,0 @@
|
|||
function [nodes,weights] = spherical_radial_sigma_points(n)
|
||||
%
|
||||
% Computes nodes and weigths from a third-degree spherical-radial cubature
|
||||
% rule.
|
||||
% INPUTS
|
||||
% n [integer] scalar, number of variables.
|
||||
%
|
||||
% OUTPUTS
|
||||
% nodes [double] nodes of the cubature
|
||||
% weigths [double] associated weigths
|
||||
%
|
||||
% REFERENCES
|
||||
%
|
||||
% Arasaratnam & Haykin 2008,2009.
|
||||
%
|
||||
% NOTES
|
||||
%
|
||||
% Copyright (C) 2009-2012 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
nodes = (sqrt(n)*([eye(n) -eye(n)]))' ;
|
||||
weights = (1/(2*n)) ;
|
||||
|
|
@ -1,237 +0,0 @@
|
|||
function return_resample = traditional_resampling(particles,weights,noise)
|
||||
% Resamples particles.
|
||||
|
||||
%@info:
|
||||
%! @deftypefn {Function File} {@var{indx} =} traditional_resampling (@var{weights},@var{noise})
|
||||
%! @anchor{particle/traditional_resampling}
|
||||
%! @sp 1
|
||||
%! Resamples particles (Resampling à la Kitagawa or stratified resampling).
|
||||
%! @sp 2
|
||||
%! @strong{Inputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item weights
|
||||
%! n*1 vector of doubles, particles' weights.
|
||||
%! @item noise
|
||||
%! n*1 vector of doubles sampled from a [0,1] uniform distribution (stratified resampling) or scalar double
|
||||
%! sampled from a [0,1] uniform distribution (Kitagawa resampling).
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{Outputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item indx
|
||||
%! n*1 vector of intergers, indices.
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{This function is called by:}
|
||||
%! @sp 1
|
||||
%! @ref{particle/resample}
|
||||
%! @sp 2
|
||||
%! @strong{This function calls:}
|
||||
%! @sp 2
|
||||
%! @end deftypefn
|
||||
%@eod:
|
||||
|
||||
% Copyright (C) 2011-2013 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
% AUTHOR(S) frederic DOT karame AT univ DASH evry DOT fr
|
||||
% stephane DOT adjemian AT univ DASH lemans DOT fr
|
||||
|
||||
% What is the number of particles?
|
||||
number_of_particles = length(weights);
|
||||
|
||||
% Initialize the returned argument.
|
||||
indx = ones(number_of_particles,1);
|
||||
|
||||
% Select method.
|
||||
switch length(noise)
|
||||
case 1
|
||||
kitagawa_resampling = 1;
|
||||
case number_of_particles
|
||||
kitagawa_resampling = 0;
|
||||
otherwise
|
||||
error(['particle::resampling: Unknown method! The size of the second argument (' inputname(3) ') is wrong.'])
|
||||
end
|
||||
|
||||
% Get the empirical CDF.
|
||||
c = cumsum(weights);
|
||||
|
||||
% Draw a starting point.
|
||||
if kitagawa_resampling
|
||||
randvec = (transpose(1:number_of_particles)-1+noise(:))/number_of_particles ;
|
||||
else
|
||||
randvec = fliplr(cumprod(noise.^(1./(number_of_particles:-1:1))));
|
||||
end
|
||||
|
||||
% Start at the bottom of the CDF
|
||||
if kitagawa_resampling
|
||||
j = 1;
|
||||
for i=1:number_of_particles
|
||||
while (randvec(i)>c(j))
|
||||
j = j+1;
|
||||
end
|
||||
indx(i) = j;
|
||||
end
|
||||
else
|
||||
for i=1:number_of_particles
|
||||
indx(i) = sum(randvec(i)>c);
|
||||
end
|
||||
% Matlab's indices start at 1...
|
||||
indx = indx+1;
|
||||
end
|
||||
|
||||
if particles==0
|
||||
return_resample = indx ;
|
||||
else
|
||||
return_resample = particles(indx,:) ;
|
||||
end
|
||||
|
||||
%@test:1
|
||||
%$ % Define the weights
|
||||
%$ weights = randn(2000,1).^2;
|
||||
%$ weights = weights/sum(weights);
|
||||
%$ % Initialize t.
|
||||
%$ t = ones(2,1);
|
||||
%$
|
||||
%$ % First, try the stratified resampling.
|
||||
%$ try
|
||||
%$ indx1 = traditional_resampling(weights,rand(2000,1));
|
||||
%$ catch
|
||||
%$ t(1) = 0;
|
||||
%$ end
|
||||
%$
|
||||
%$ % Second, try the Kitagawa resampling.
|
||||
%$ try
|
||||
%$ indx2 = traditional_resampling(weights,rand);
|
||||
%$ catch
|
||||
%$ t(2) = 0;
|
||||
%$ end
|
||||
%$
|
||||
%$ T = all(t);
|
||||
%@eof:1
|
||||
|
||||
%@test:2
|
||||
%$ % Define the weights
|
||||
%$ weights = exp(randn(2000,1));
|
||||
%$ weights = weights/sum(weights);
|
||||
%$ % Initialize t.
|
||||
%$ t = ones(2,1);
|
||||
%$
|
||||
%$ % First, try the stratified resampling.
|
||||
%$ try
|
||||
%$ indx1 = traditional_resampling(weights,rand(2000,1));
|
||||
%$ catch
|
||||
%$ t(1) = 0;
|
||||
%$ end
|
||||
%$
|
||||
%$ % Second, try the Kitagawa resampling.
|
||||
%$ try
|
||||
%$ indx2 = traditional_resampling(weights,rand);
|
||||
%$ catch
|
||||
%$ t(2) = 0;
|
||||
%$ end
|
||||
%$
|
||||
%$ T = all(t);
|
||||
%@eof:2
|
||||
|
||||
%@test:3
|
||||
%$ % Set the number of particles.
|
||||
%$ number_of_particles = 20000;
|
||||
%$
|
||||
%$ show_plot = 0;
|
||||
%$ show_time = 1;
|
||||
%$
|
||||
%$ % Define the weights
|
||||
%$ weights = randn(number_of_particles,1).^2;
|
||||
%$ weights = weights/sum(weights);
|
||||
%$
|
||||
%$ % Compute the empirical CDF
|
||||
%$ c = cumsum(weights);
|
||||
%$
|
||||
%$ % Stratified resampling.
|
||||
%$ noise = rand(number_of_particles,1);
|
||||
%$
|
||||
%$ if show_time
|
||||
%$ disp('Stratified resampling timing:')
|
||||
%$ tic
|
||||
%$ end
|
||||
%$
|
||||
%$ indx1 = traditional_resampling(weights,noise);
|
||||
%$
|
||||
%$ if show_time
|
||||
%$ toc
|
||||
%$ tic
|
||||
%$ end
|
||||
%$
|
||||
%$ indx1_ = zeros(number_of_particles,1);
|
||||
%$ randvec = (transpose(1:number_of_particles)-1+noise)/number_of_particles;
|
||||
%$ for i=1:number_of_particles
|
||||
%$ j = 1;
|
||||
%$ while (randvec(i)>c(j))
|
||||
%$ j = j + 1;
|
||||
%$ end
|
||||
%$ indx1_(i) = j;
|
||||
%$ end
|
||||
%$
|
||||
%$ if show_time
|
||||
%$ toc
|
||||
%$ end
|
||||
%$
|
||||
%$ % Kitagawa's resampling.
|
||||
%$ noise = rand;
|
||||
%$
|
||||
%$ if show_time
|
||||
%$ disp('Kitagawa''s resampling timing:')
|
||||
%$ tic
|
||||
%$ end
|
||||
%$
|
||||
%$ indx2 = traditional_resampling(weights,noise);
|
||||
%$
|
||||
%$ if show_time
|
||||
%$ toc
|
||||
%$ tic
|
||||
%$ end
|
||||
%$
|
||||
%$ indx2_ = zeros(number_of_particles,1);
|
||||
%$ randvec = (transpose(1:number_of_particles)-1+noise)/number_of_particles;
|
||||
%$ j = 1;
|
||||
%$ for i=1:number_of_particles
|
||||
%$ while (randvec(i)>c(j))
|
||||
%$ j = j + 1;
|
||||
%$ end
|
||||
%$ indx2_(i) = j;
|
||||
%$ end
|
||||
%$
|
||||
%$ if show_time
|
||||
%$ toc
|
||||
%$ end
|
||||
%$
|
||||
%$ % REMARK
|
||||
%$ % Note that the alternative code used in this test is sensibly faster than the code proposed
|
||||
%$ % in the routine for the resampling scheme à la Kitagawa...
|
||||
%$
|
||||
%$ if show_plot
|
||||
%$ plot(randvec,c,'-r'), hold on, plot([randvec(1),randvec(end)],[c(1),c(end)],'-k'), hold off, axis tight, box on
|
||||
%$ end
|
||||
%$
|
||||
%$ % Check results.
|
||||
%$ t(1) = dassert(indx1,indx1_);
|
||||
%$ t(2) = dassert(indx2,indx2_);
|
||||
%$ T = all(t);
|
||||
%@eof:3
|
||||
|
|
@ -1,82 +0,0 @@
|
|||
function new_particles = univariate_smooth_resampling(weights,particles,number_of_new_particles)
|
||||
% Smooth Resampling of the particles.
|
||||
|
||||
%@info:
|
||||
%! @deftypefn {Function File} {@var{new_particles} =} univariate_smooth_resampling (@var{weights}, @var{number_of_new_particles})
|
||||
%! @anchor{particle/univariate_smooth_resampling}
|
||||
%! @sp 1
|
||||
%! Smooth Resampling of the particles (univariate version).
|
||||
%! @sp 2
|
||||
%! @strong{Inputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item weights
|
||||
%! n*1 vector of doubles, particles' weights.
|
||||
%! @item particles
|
||||
%! n*1 vector of doubles, particles.
|
||||
%! @item number_of_new_particles
|
||||
%! Integer scalar.
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{Outputs}
|
||||
%! @sp 1
|
||||
%! @table @ @var
|
||||
%! @item indx
|
||||
%! number_of_new_particles*1 vector of doubles, new particles.
|
||||
%! @end table
|
||||
%! @sp 2
|
||||
%! @strong{This function is called by:}
|
||||
%! @sp 1
|
||||
%! @ref{particle/sequantial_importance_particle_filter}
|
||||
%! @sp 2
|
||||
%! @strong{This function calls:}
|
||||
%! @sp 2
|
||||
%! @end deftypefn
|
||||
%@eod:
|
||||
|
||||
% Copyright (C) 2012 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
% AUTHOR(S) frederic DOT karame AT univ DASH lemans DOT fr
|
||||
% stephane DOT adjemian AT univ DASH lemans DOT fr
|
||||
|
||||
M = length(particles) ;
|
||||
lambda_tilde = [ (.5*weights(1)) ;
|
||||
(.5*(weights(1:M-1)+weights(2:M))) ;
|
||||
(.5*weights(M)) ] ;
|
||||
lambda_bar = cumsum(lambda_tilde) ;
|
||||
u = rand(1,1) ;
|
||||
new_particles = zeros(number_of_new_particles,1) ;
|
||||
rj = 0 ;
|
||||
i = 1 ;
|
||||
j = 1 ;
|
||||
while i<=number_of_new_particles
|
||||
u_j = ( i-1 + u)/number_of_new_particles ;
|
||||
while u_j>lambda_bar(j)
|
||||
rj = j ;
|
||||
j = j+1 ;
|
||||
end
|
||||
if rj==0
|
||||
new_particles(i) = particles(1) ;
|
||||
elseif rj==M
|
||||
new_particles(i) = particles(M) ;
|
||||
else
|
||||
u_star = (u_j - lambda_bar(rj))./lambda_tilde(rj+1) ;
|
||||
new_particles(i) = (particles(rj+1) - particles(rj))*u_star + particles(rj) ;
|
||||
end
|
||||
i = i+1 ;
|
||||
end
|
||||
|
|
@ -1,42 +0,0 @@
|
|||
function [nodes,W_m,W_c] = unscented_sigma_points(n,DynareOptions)
|
||||
%
|
||||
% Computes nodes and weigths for a scaled unscented transform cubature
|
||||
% INPUTS
|
||||
% n [integer] scalar, number of variables.
|
||||
%
|
||||
% OUTPUTS
|
||||
% nodes [double] nodes of the cubature
|
||||
% weigths [double] associated weigths
|
||||
%
|
||||
% REFERENCES
|
||||
%
|
||||
%
|
||||
%
|
||||
% NOTES
|
||||
%
|
||||
% Copyright (C) 2009-2012 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
lambda = (DynareOptions.particle.unscented.alpha^2)*(n+DynareOptions.particle.unscented.kappa) - n ;
|
||||
nodes = [ zeros(n,1) ( sqrt(n+lambda).*([ eye(n) -eye(n)]) ) ]' ;
|
||||
W_m = lambda/(n+lambda) ;
|
||||
W_c = W_m + (1-DynareOptions.particle.unscented.alpha^2+DynareOptions.particle.unscented.beta) ;
|
||||
temp = ones(2*n,1)/(2*(n+lambda)) ;
|
||||
W_m = [W_m ; temp] ;
|
||||
W_c = [W_c ; temp] ;
|
||||
|
||||
|
||||
|
|
@ -0,0 +1 @@
|
|||
Subproject commit b577de9b871c74e19d4509047f0d6f24dab06419
|
||||
Loading…
Reference in New Issue