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Allow k order approximation in nonlinear Kalman Filter (nlkf). 

Ref. dynare#1673
remove-submodule^2
Stéphane Adjemian (Charybdis) 2019-12-21 10:44:23 +01:00
parent 53a9700f81
commit 479a37f9cd
1 changed files with 35 additions and 48 deletions
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83
nonlinear-filters/src/nonlinear_kalman_filter.m
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@ -1,4 +1,5 @@
function [LIK,lik] = nonlinear_kalman_filter(ReducedForm, Y, start, ParticleOptions, ThreadsOptions)
function [LIK,lik] = nonlinear_kalman_filter(ReducedForm, Y, start, ParticleOptions, ThreadsOptions, DynareOptions, Model)
% Evaluates the likelihood of a non-linear model approximating the
% predictive (prior) and filtered (posterior) densities for state variables
% by a Kalman filter.
@ -30,7 +31,8 @@ function [LIK,lik] = nonlinear_kalman_filter(ReducedForm, Y, start, ParticleOpti
%
% NOTES
% The vector "lik" is used to evaluate the jacobian of the likelihood.
% Copyright (C) 2009-2017 Dynare Team
% Copyright (C) 2009-2019 Dynare Team
%
% This file is part of Dynare.
%
@ -47,55 +49,41 @@ function [LIK,lik] = nonlinear_kalman_filter(ReducedForm, Y, start, ParticleOpti
% 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 nodes weights weights_c
persistent sample_size number_of_state_variables number_of_observed_variables number_of_structural_innovations
% Set default
if isempty(start)
start = 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;
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
if ReducedForm.use_k_order_solver
dr = ReducedForm.dr;
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;
end
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);
init_flag = 1;
end
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);
% compute gaussian quadrature nodes and weights on states and shocks
if ParticleOptions.proposal_approximation.montecarlo
nodes = randn(ParticleOptions.number_of_particles,number_of_state_variables+number_of_structural_innovations) ;
weights = 1/ParticleOptions.number_of_particles ;
weights_c = weights ;
nodes = randn(ParticleOptions.number_of_particles,number_of_state_variables+number_of_structural_innovations);
weights = 1/ParticleOptions.number_of_particles;
weights_c = weights;
elseif ParticleOptions.proposal_approximation.cubature
[nodes,weights] = spherical_radial_sigma_points(number_of_state_variables+number_of_structural_innovations) ;
weights_c = weights ;
[nodes,weights] = spherical_radial_sigma_points(number_of_state_variables+number_of_structural_innovations);
weights_c = weights;
elseif ParticleOptions.proposal_approximation.unscented
[nodes,weights,weights_c] = unscented_sigma_points(number_of_state_variables+number_of_structural_innovations,ParticleOptions);
else
@ -120,27 +108,28 @@ lik = NaN(sample_size,1);
LIK = NaN;
for t=1:sample_size
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 ] ];
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,ThreadsOptions.local_state_space_iteration_2);
if ReducedForm.use_k_order_solver
tmp = local_state_space_iteration_k(yhat, epsilon, dr, Model, DynareOptions);
else
tmp = local_state_space_iteration_2(yhat, epsilon, ghx, ghu, constant, ghxx, ghuu, ghxu, ThreadsOptions.local_state_space_iteration_2);
end
PredictedStateMean = tmp(mf0,:)*weights ;
PredictedObservedMean = tmp(mf1,:)*weights;
if ParticleOptions.proposal_approximation.cubature || ParticleOptions.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] = 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));
@ -162,16 +151,14 @@ for t=1:sample_size
lik(t)=-Inf;
return
end
[PredictedObservedVarianceSquareRoot, p]= chol(PredictedObservedVariance,'lower');
[~, p]= chol(PredictedObservedVariance,'lower');
if p
LIK=-Inf;
lik(t)=-Inf;
return
end
end
% lik(t) = log( probability2(0,PredictedObservedVarianceSquareRoot,PredictionError) ) ;
lik(t) = log( sum(probability2(Y(:,t),H_lower_triangular_cholesky,tmp(mf1,:)).*weights,1) ) ;
% lik(t) = log(sum(probability2(Y(:,t),PredictedObservedVarianceSquareRoot,tmp(mf1,:)).*weights,1) ) ;
end
LIK = -sum(lik(start:end));
LIK = -sum(lik(start:end));