186 lines
7.2 KiB
Matlab
186 lines
7.2 KiB
Matlab
function [LIK,lik] = sequential_importance_particle_filter(ReducedForm,Y,start,ParticleOptions,ThreadsOptions, options_, M_)
|
|
|
|
% Evaluates the likelihood of a nonlinear model with a particle filter (optionally with resampling).
|
|
|
|
% Copyright © 2011-2022 Dynare Team
|
|
%
|
|
% This file is part of Dynare (particles module).
|
|
%
|
|
% 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 particles module 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 <https://www.gnu.org/licenses/>.
|
|
|
|
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 = ParticleOptions.pruning;
|
|
|
|
% Get steady state and mean.
|
|
steadystate = ReducedForm.steadystate;
|
|
constant = ReducedForm.constant;
|
|
state_variables_steady_state = ReducedForm.state_variables_steady_state;
|
|
|
|
order = options_.order;
|
|
|
|
% 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 = ParticleOptions.number_of_particles;
|
|
init_flag = 1;
|
|
end
|
|
|
|
if ReducedForm.use_k_order_solver
|
|
dr = ReducedForm.dr;
|
|
udr = ReducedForm.udr;
|
|
else
|
|
% 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;
|
|
ghs2 = ReducedForm.ghs2;
|
|
if order == 3
|
|
% Set local state space model (third order approximation).
|
|
ghxxx = ReducedForm.ghxxx;
|
|
ghuuu = ReducedForm.ghuuu;
|
|
ghxxu = ReducedForm.ghxxu;
|
|
ghxuu = ReducedForm.ghxuu;
|
|
ghxss = ReducedForm.ghxss;
|
|
ghuss = ReducedForm.ghuss;
|
|
end
|
|
end
|
|
|
|
% 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 +log(det(H)) ;
|
|
lik = NaN(sample_size,1);
|
|
|
|
% Get initial condition for the state vector.
|
|
StateVectorMean = ReducedForm.StateVectorMean;
|
|
StateVectorVarianceSquareRoot = chol(ReducedForm.StateVectorVariance)';%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().
|
|
options_=set_dynare_seed_local_options(options_,'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
|
|
if order == 2
|
|
StateVectors_ = StateVectors;
|
|
state_variables_steady_state_ = state_variables_steady_state;
|
|
mf0_ = mf0;
|
|
elseif order == 3
|
|
StateVectors_ = repmat(StateVectors,3,1);
|
|
state_variables_steady_state_ = repmat(state_variables_steady_state,3,1);
|
|
mf0_ = repmat(mf0,1,3);
|
|
mask2 = number_of_state_variables+1:2*number_of_state_variables;
|
|
mask3 = 2*number_of_state_variables+1:3*number_of_state_variables;
|
|
mf0_(mask2) = mf0_(mask2)+size(ghx,1);
|
|
mf0_(mask3) = mf0_(mask3)+2*size(ghx,1);
|
|
else
|
|
error('Pruning is not available for orders > 3');
|
|
end
|
|
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_);
|
|
if order == 2
|
|
[tmp, tmp_] = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,ThreadsOptions.local_state_space_iteration_2);
|
|
elseif order == 3
|
|
[tmp, tmp_] = local_state_space_iteration_3(yhat_, epsilon, ghx, ghu, ghxx, ghuu, ghxu, ghs2, ghxxx, ghuuu, ghxxu, ghxuu, ghxss, ghuss, steadystate, ThreadsOptions.local_state_space_iteration_3, pruning);
|
|
else
|
|
error('Pruning is not available for orders > 3');
|
|
end
|
|
else
|
|
if ReducedForm.use_k_order_solver
|
|
tmp = local_state_space_iteration_k(yhat, epsilon, dr, M_, options_, udr);
|
|
else
|
|
if order == 2
|
|
tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,ThreadsOptions.local_state_space_iteration_2);
|
|
elseif order == 3
|
|
tmp = local_state_space_iteration_3(yhat, epsilon, ghx, ghu, ghxx, ghuu, ghxu, ghs2, ghxxx, ghuuu, ghxxu, ghxuu, ghxss, ghuss, steadystate, ThreadsOptions.local_state_space_iteration_3, pruning);
|
|
else
|
|
error('Order > 3: use_k_order_solver should be set to true');
|
|
end
|
|
end
|
|
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;
|
|
%PredictedObservedVariance = H;
|
|
if rcond(H) > 1e-16
|
|
lnw = -.5*(const_lik+sum(PredictionError.*(H\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 (ParticleOptions.resampling.status.generic && neff(weights)<ParticleOptions.resampling.threshold*sample_size) || ParticleOptions.resampling.status.systematic
|
|
if pruning
|
|
temp = resample([tmp(mf0,:)' tmp_(mf0_,:)'],weights',ParticleOptions);
|
|
StateVectors = temp(:,1:number_of_state_variables)';
|
|
StateVectors_ = temp(:,number_of_state_variables+1:end)';
|
|
else
|
|
StateVectors = resample(tmp(mf0,:)',weights',ParticleOptions)';
|
|
end
|
|
weights = ones(1,number_of_particles)/number_of_particles;
|
|
elseif ParticleOptions.resampling.status.none
|
|
StateVectors = tmp(mf0,:);
|
|
if pruning
|
|
StateVectors_ = tmp_(mf0_,:);
|
|
end
|
|
end
|
|
end
|
|
|
|
LIK = -sum(lik(start:end));
|