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Estimation with analytic scores and hessian; 

This includes re-setting the list of output arguments in objective functions
Added test function
time-shift
Marco Ratto 2012-04-27 15:57:58 +02:00 committed by Michel Juillard
parent 3332a7f794
commit da9ec0f187
22 changed files with 953 additions and 80 deletions
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5
matlab/DsgeVarLikelihood.m
View File

@ -1,4 +1,4 @@
function [fval,exit_flag,info,PHI,SIGMAu,iXX,prior] = DsgeVarLikelihood(xparam1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults)
function [fval,grad,hess,exit_flag,info,PHI,SIGMAu,iXX,prior] = DsgeVarLikelihood(xparam1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults)
% Evaluates the posterior kernel of the bvar-dsge model.
%
% INPUTS
@ -37,6 +37,9 @@ function [fval,exit_flag,info,PHI,SIGMAu,iXX,prior] = DsgeVarLikelihood(xparam1,
% Declaration of the persistent variables.
persistent penalty dsge_prior_weight_idx
grad=[];
hess=[];
% Initialization of the penalty
if ~nargin || isempty(penalty)
penalty = 1e8;

29
matlab/csminwel1.m
View File

@ -63,7 +63,7 @@ snit=100;
% stailstr=[' P' num2str(i) stailstr];
%end
[f0,cost_flag] = feval(fcn,x0,varargin{:});
[f0,junk1,junk2,cost_flag] = feval(fcn,x0,varargin{:});
if ~cost_flag
disp('Bad initial parameter.')
@ -79,8 +79,11 @@ if NumGrad
case 5
[g,badg] = numgrad5(fcn, f0, x0, epsilon, varargin{:});
end
else
elseif ischar(grad)
[g,badg] = feval(grad,x0,varargin{:});
else
g=junk1;
badg=0;
end
retcode3=101;
x=x0;
@ -126,8 +129,11 @@ while ~done
case 5
[g1,badg1] = numgrad5(fcn, f1, x1, epsilon, varargin{:});
end
else
elseif ischar(grad),
[g1 badg1] = feval(grad,x1,varargin{:});
else
[junk1,g1,junk2, cost_flag] = feval(fcn,x1,varargin{:});
badg1 = ~cost_flag;
end
wall1=badg1;
% g1
@ -160,8 +166,11 @@ while ~done
case 5
[g2,badg2] = numgrad5(fcn, f2, x2, epsilon, varargin{:});
end
else
elseif ischar(grad),
[g2 badg2] = feval(grad,x2,varargin{:});
else
[junk1,g2,junk2, cost_flag] = feval(fcn,x1,varargin{:});
badg2 = ~cost_flag;
end
wall2=badg2;
% g2
@ -195,8 +204,11 @@ while ~done
case 5
[g3,badg3] = numgrad5(fcn, f3, x3, epsilon, varargin{:});
end
else
elseif ischar(grad),
[g3 badg3] = feval(grad,x3,varargin{:});
else
[junk1,g3,junk2, cost_flag] = feval(fcn,x1,varargin{:});
badg3 = ~cost_flag;
end
wall3=badg3;
% g3
@ -259,8 +271,11 @@ while ~done
case 5
[gh,badgh] = numgrad5(fcn, fh, xh, epsilon, varargin{:});
end
else
elseif ischar(grad),
[gh badgh] = feval(grad, xh,varargin{:});
else
[junk1,gh,junk2, cost_flag] = feval(fcn,x1,varargin{:});
badgh = ~cost_flag;
end
end
badgh=1;
@ -273,7 +288,7 @@ while ~done
%badgh
stuck = (abs(fh-f) < crit);
if (~badg) && (~badgh) && (~stuck)
H = bfgsi1(H,gh-g,xh-x);
H = bfgsi(H,gh-g,xh-x);
end
if Verbose
disp('----')

98
matlab/dsge_likelihood.m
View File

@ -1,4 +1,4 @@
function [fval,exit_flag,ys,trend_coeff,info,Model,DynareOptions,BayesInfo,DynareResults,DLIK,AHess] = dsge_likelihood(xparam1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults,derivatives_info)
function [fval,DLIK,Hess,exit_flag,ys,trend_coeff,info,Model,DynareOptions,BayesInfo,DynareResults] = dsge_likelihood(xparam1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults,derivatives_info)
% Evaluates the posterior kernel of a dsge model.
%@info:
@ -151,7 +151,7 @@ exit_flag = 1;
info = 0;
singularity_flag = 0;
DLIK = [];
AHess = [];
Hess = [];
if DynareOptions.estimation_dll
[fval,exit_flag,ys,trend_coeff,info,params,H,Q] ...
@ -167,12 +167,11 @@ if DynareOptions.estimation_dll
end
% Set flag related to analytical derivatives.
if nargout > 9
analytic_derivation=1;
else
analytic_derivation = DynareOptions.analytic_derivation;
if nargout==1,
analytic_derivation=0;
end
%------------------------------------------------------------------------------
% 1. Get the structural parameters & define penalties
%------------------------------------------------------------------------------
@ -183,6 +182,9 @@ if ~isequal(DynareOptions.mode_compute,1) && any(xparam1<BayesInfo.lb)
fval = penalty+sum((BayesInfo.lb(k)-xparam1(k)).^2);
exit_flag = 0;
info = 41;
if analytic_derivation,
DLIK=ones(length(xparam1),1);
end
return
end
@ -192,6 +194,9 @@ if ~isequal(DynareOptions.mode_compute,1) && any(xparam1>BayesInfo.ub)
fval = penalty+sum((xparam1(k)-BayesInfo.ub(k)).^2);
exit_flag = 0;
info = 42;
if analytic_derivation,
DLIK=ones(length(xparam1),1);
end
return
end
@ -282,11 +287,17 @@ if info(1) == 1 || info(1) == 2 || info(1) == 5 || info(1) == 7 || info(1) == 22
fval = penalty+1;
info = info(1);
exit_flag = 0;
if analytic_derivation,
DLIK=ones(length(xparam1),1);
end
return
elseif info(1) == 3 || info(1) == 4 || info(1)==6 ||info(1) == 19 || info(1) == 20 || info(1) == 21 || info(1) == 23
fval = penalty+info(2);
info = info(1);
exit_flag = 0;
if analytic_derivation,
DLIK=ones(length(xparam1),1);
end
return
end
@ -472,7 +483,11 @@ end
if analytic_derivation
no_DLIK = 0;
full_Hess = 0;
full_Hess = analytic_derivation==2;
asy_Hess = analytic_derivation==-2;
if asy_Hess,
analytic_derivation=1;
end
DLIK = [];
AHess = [];
if nargin<8 || isempty(derivatives_info)
@ -489,9 +504,9 @@ if analytic_derivation
end
if full_Hess,
[dum, DT, DOm, DYss, dum2, D2T, D2Om, D2Yss] = getH(A, B, Model,DynareResults,0,indparam,indexo);
[dum, DT, DOm, DYss, dum2, D2T, D2Om, D2Yss] = getH(A, B, Model,DynareResults,0,indparam,indexo);
else
[dum, DT, DOm, DYss] = getH(A, B, Model,DynareResults,0,indparam,indexo);
[dum, DT, DOm, DYss] = getH(A, B, Model,DynareResults,0,indparam,indexo);
end
else
DT = derivatives_info.DT;
@ -576,6 +591,13 @@ if analytic_derivation
end
end
end
if analytic_derivation==1,
analytic_deriv_info={analytic_derivation,DT,DYss,DOm,DH,DP};
else
analytic_deriv_info={analytic_derivation,DT,DYss,DOm,DH,DP,D2T,D2Yss,D2Om,D2H,D2P};
end
else
analytic_deriv_info={0};
end
%------------------------------------------------------------------------------
@ -592,19 +614,9 @@ if ((kalman_algo==1) || (kalman_algo==3))% Multivariate Kalman Filter
a,Pstar, ...
kalman_tol, riccati_tol, ...
DynareOptions.presample, ...
T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods);
end
if analytic_derivation
if no_DLIK==0
[DLIK] = score(T,R,Q,H,Pstar,Y,DT,DYss,DOm,DH,DP,start,Z,kalman_tol,riccati_tol);
end
if nargout==11
[AHess] = AHessian(T,R,Q,H,Pstar,Y,DT,DYss,DOm,DH,DP,start,Z,kalman_tol,riccati_tol);
if full_Hess,
Hess = get_Hessian(T,R,Q,H,Pstar,Y,DT,DYss,DOm,DH,DP,D2T,D2Yss,D2Om,D2H,D2P,start,Z,kalman_tol,riccati_tol);
Hess0 = getHessian(Y,T,DT,D2T, R*Q*transpose(R),DOm,D2Om,Z,DYss,D2Yss);
end
end
T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods, ...
analytic_deriv_info{:});
end
else
[LIK,lik] = missing_observations_kalman_filter(DynareDataset.missing.aindex,DynareDataset.missing.number_of_observations,DynareDataset.missing.no_more_missing_observations,Y,diffuse_periods+1,size(Y,2), ...
@ -613,6 +625,10 @@ if ((kalman_algo==1) || (kalman_algo==3))% Multivariate Kalman Filter
DynareOptions.presample, ...
T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods);
end
if analytic_derivation,
LIK1=LIK;
LIK=LIK1{1};
end
if isinf(LIK)
if kalman_algo == 1
kalman_algo = 2;
@ -636,10 +652,19 @@ if (kalman_algo==2) || (kalman_algo==4)
if isequal(H,0)
H = zeros(pp,1);
mmm = mm;
if analytic_derivation,
DH = zeros(pp,length(xparam1));
end
else
if all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
H = diag(H);
mmm = mm;
if analytic_derivation,
for j=1:pp,
tmp(j,:)=DH(j,j,:);
end
DH=tmp;
end
else
Z = [Z, eye(pp)];
T = blkdiag(T,zeros(pp));
@ -651,6 +676,9 @@ if (kalman_algo==2) || (kalman_algo==4)
mmm = mm+pp;
end
end
if analytic_derivation,
analytic_deriv_info{5}=DH;
end
end
[LIK, lik] = univariate_kalman_filter(DynareDataset.missing.aindex,DynareDataset.missing.number_of_observations,DynareDataset.missing.no_more_missing_observations,Y,diffuse_periods+1,size(Y,2), ...
@ -658,7 +686,11 @@ if (kalman_algo==2) || (kalman_algo==4)
DynareOptions.kalman_tol, ...
DynareOptions.riccati_tol, ...
DynareOptions.presample, ...
T,Q,R,H,Z,mmm,pp,rr,Zflag,diffuse_periods);
T,Q,R,H,Z,mmm,pp,rr,Zflag,diffuse_periods,analytic_deriv_info{:});
if analytic_derivation,
LIK1=LIK;
LIK=LIK1{1};
end
if DynareOptions.lik_init==3
LIK = LIK+dLIK;
if analytic_derivation==0 && nargout==2,
@ -667,6 +699,22 @@ if (kalman_algo==2) || (kalman_algo==4)
end
end
if analytic_derivation
if no_DLIK==0
DLIK = LIK1{2};
% [DLIK] = score(T,R,Q,H,Pstar,Y,DT,DYss,DOm,DH,DP,start,Z,kalman_tol,riccati_tol);
end
if full_Hess,
Hess = -LIK1{3};
% [Hess, DLL] = get_Hessian(T,R,Q,H,Pstar,Y,DT,DYss,DOm,DH,DP,D2T,D2Yss,D2Om,D2H,D2P,start,Z,kalman_tol,riccati_tol);
% Hess0 = getHessian(Y,T,DT,D2T, R*Q*transpose(R),DOm,D2Om,Z,DYss,D2Yss);
end
if asy_Hess,
[Hess] = AHessian(T,R,Q,H,Pstar,Y,DT,DYss,DOm,DH,DP,start,Z,kalman_tol,riccati_tol);
end
end
if isnan(LIK)
info = 45;
exit_flag = 0;
@ -684,7 +732,7 @@ end
if analytic_derivation
if full_Hess,
[lnprior, dlnprior, d2lnprior] = priordens(xparam1,BayesInfo.pshape,BayesInfo.p6,BayesInfo.p7,BayesInfo.p3,BayesInfo.p4);
AHess = Hess + d2lnprior;
Hess = Hess - d2lnprior;
else
[lnprior, dlnprior] = priordens(xparam1,BayesInfo.pshape,BayesInfo.p6,BayesInfo.p7,BayesInfo.p3,BayesInfo.p4);
end
@ -705,4 +753,4 @@ penalty = fval;
if analytic_derivation==0 && nargout==2,
lik=lik(start:end,:);
DLIK=[-lnprior; lik(:)];
end
end

10
matlab/dynare_estimation.m
View File

@ -53,6 +53,12 @@ end
M_.dname = dname;
if options_.mode_compute && options_.analytic_derivation,
analytic_derivation0=options_.analytic_derivation;
options_.analytic_derivation=1;
end
if nnobs > 1
for i=1:nnobs
options_.nobs = nobs(i);
@ -64,6 +70,10 @@ else
dynare_estimation_1(var_list,dname);
end
if options_.mode_compute && options_.analytic_derivation,
options_.analytic_derivation=analytic_derivation0;
end
if nnobs > 1 && horizon > 0
mh_replic = options_.mh_replic;
rawdata = read_variables(options_.datafile,options_.varobs,[],options_.xls_sheet,options_.xls_range);

30
matlab/dynare_estimation_1.m
View File

@ -167,6 +167,9 @@ if ~isequal(options_.mode_compute,0) && ~options_.mh_posterior_mode_estimation
'MaxFunEvals',100000,'TolFun',1e-8,'TolX',1e-6);
if isfield(options_,'optim_opt')
eval(['optim_options = optimset(optim_options,' options_.optim_opt ');']);
end
if options_.analytic_derivation,
optim_options = optimset(optim_options,'GradObj','on');
end
[xparam1,fval,exitflag,output,lamdba,grad,hessian_fmincon] = ...
fmincon(objective_function,xparam1,[],[],[],[],lb,ub,[],optim_options,dataset_,options_,M_,estim_params_,bayestopt_,oo_);
@ -177,14 +180,23 @@ if ~isequal(options_.mode_compute,0) && ~options_.mh_posterior_mode_estimation
if isfield(options_,'optim_opt')
eval(['optim_options = optimset(optim_options,' options_.optim_opt ');']);
end
if options_.analytic_derivation,
optim_options = optimset(optim_options,'GradObj','on');
end
[xparam1,fval,exitflag] = fminunc(objective_function,xparam1,optim_options,dataset_,options_,M_,estim_params_,bayestopt_,oo_);
case 4
H0 = 1e-4*eye(nx);
crit = 1e-7;
nit = 1000;
verbose = 2;
if options_.analytic_derivation,
analytic_grad=1;
else
analytic_grad=[];
end
[fval,xparam1,grad,hessian_csminwel,itct,fcount,retcodehat] = ...
csminwel1(objective_function,xparam1,H0,[],crit,nit,options_.gradient_method,options_.gradient_epsilon,dataset_,options_,M_,estim_params_,bayestopt_,oo_);
csminwel1(objective_function,xparam1,H0,analytic_grad,crit,nit,options_.gradient_method,options_.gradient_epsilon,dataset_,options_,M_,estim_params_,bayestopt_,oo_);
disp(sprintf('Objective function at mode: %f',fval))
case 5
if isfield(options_,'hess')
@ -350,8 +362,17 @@ if ~isequal(options_.mode_compute,0) && ~options_.mh_posterior_mode_estimation
end
if ~isequal(options_.mode_compute,6) && ~isequal(options_.mode_compute,'prior')
if options_.cova_compute == 1
hh = reshape(hessian(objective_function,xparam1, ...
options_.gstep,dataset_,options_,M_,estim_params_,bayestopt_,oo_),nx,nx);
if options_.analytic_derivation && strcmp(func2str(objective_function),'dsge_likelihood'),
ana_deriv = options_.analytic_derivation;
options_.analytic_derivation = 2;
[junk1, junk2, hh] = feval(objective_function,xparam1, ...
dataset_,options_,M_,estim_params_,bayestopt_,oo_);
options_.analytic_derivation = ana_deriv;
else
hh = reshape(hessian(objective_function,xparam1, ...
options_.gstep,dataset_,options_,M_,estim_params_,bayestopt_,oo_),nx,nx);
end
end
end
parameter_names = bayestopt_.name;
@ -865,11 +886,14 @@ if (any(bayestopt_.pshape >0 ) && options_.mh_replic) || ...
if options_.load_mh_file && options_.use_mh_covariance_matrix
invhess = compute_mh_covariance_matrix;
end
ana_deriv = options_.analytic_derivation;
options_.analytic_derivation = 0;
if options_.cova_compute
feval(options_.posterior_sampling_method,objective_function,options_.proposal_distribution,xparam1,invhess,bounds,dataset_,options_,M_,estim_params_,bayestopt_,oo_);
else
error('I Cannot start the MCMC because the hessian of the posterior kernel at the mode was not computed.')
end
options_.analytic_derivation = ana_deriv;
end
if options_.mh_posterior_mode_estimation
CutSample(M_, options_, estim_params_);

7
matlab/dynare_estimation_init.m
View File

@ -284,6 +284,13 @@ else
bayestopt_.smoother_var_list);
end;
if options_.analytic_derivation,
if ~(exist('sylvester3','file')==2),
dynareroot = strrep(which('dynare'),'dynare.m','');
addpath([dynareroot 'gensylv'])
end
end
% Test if the data file is declared.
if isempty(options_.datafile)
if gsa_flag

4
matlab/dynare_gradient.m
View File

@ -52,11 +52,11 @@ for i=1:m
else
h = H(:,i);
end
[Fh,flag] = feval(fcn, x+transpose(h), varargin{:});
[Fh,junk1,junk2,flag] = feval(fcn, x+transpose(h), varargin{:});
if flag
G(:,i) = (Fh-F)/epsilon;
else
[Fh,flag] = feval(fcn, x-transpose(h), varargin{:});
[Fh,junk1,junk2,flag] = feval(fcn, x-transpose(h), varargin{:});
if flag
G(:,i) = (F-Fh)/epsilon;
else

3
matlab/identification_analysis.m
View File

@ -131,11 +131,12 @@ if info(1)==0,
options_.order = 1;
options_.periods = data_info.info.ntobs+100;
options_.kalman_algo = 1;
options_.analytic_derivation = -2;
info = stoch_simul(options_.varobs);
data_info.data=oo_.endo_simul(options_.varobs_id,100+1:end);
% datax=data;
derivatives_info.no_DLIK=1;
[fval,cost_flag,ys,trend_coeff,info,M_,options_,bayestopt_,oo_,DLIK,AHess] = dsge_likelihood(params',data_info,options_,M_,estim_params_,bayestopt_,oo_,derivatives_info);
[fval,DLIK,AHess,cost_flag,ys,trend_coeff,info,M_,options_,bayestopt_,oo_] = dsge_likelihood(params',data_info,options_,M_,estim_params_,bayestopt_,oo_,derivatives_info);
% fval = DsgeLikelihood(xparam1,data_info,options_,M_,estim_params_,bayestopt_,oo_);
AHess=-AHess;
if min(eig(AHess))<0,

2
matlab/initial_estimation_checks.m
View File

@ -38,7 +38,7 @@ end
[DynareResults.steady_state] = evaluate_steady_state(DynareResults.steady_state,Model,DynareOptions,DynareResults,DynareOptions.diffuse_filter==0);
% Evaluate the likelihood.
[fval,a,b,c,d] = feval(objective_function,xparam1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
[fval,junk1,junk2,a,b,c,d] = feval(objective_function,xparam1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
if DynareOptions.dsge_var
info = b;

273
matlab/kalman/likelihood/computeDLIK.m Normal file
View File

@ -0,0 +1,273 @@
function [Da,DP1,DLIK,D2a,D2P1,Hesst] = computeDLIK(k,tmp,Z,Zflag,v,T,K,P,iF,Da,DYss,DT,DOm,DP,DH,notsteady,D2a,D2Yss,D2T,D2Om,D2P)
% 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) marco.ratto@jrc.ec.europa.eu
persistent DK DF D2K D2F
if notsteady
if Zflag
[DK,DF,DP1] = computeDKalmanZ(T,DT,DOm,P,DP,DH,Z,iF,K);
if nargout>3,
[D2K,D2F,D2P1] = computeD2KalmanZ(T,DT,D2T,D2Om,P,DP,D2P,DH,Z,iF,K,DK);
end
else
[DK,DF,DP1] = computeDKalman(T,DT,DOm,P,DP,DH,Z,iF,K);
if nargout>3,
[D2K,D2F,D2P1] = computeD2Kalman(T,DT,D2T,D2Om,P,DP,D2P,DH,Z,iF,K,DK);
end
end
else
DP1=DP;
if nargout>3,
D2P1=D2P;
end
end
Dv=zeros(length(v),k);
% D2v=zeros(length(v),k,k);
for ii = 1:k
if Zflag
Dv(:,ii) = -Z*Da(:,ii) - Z*DYss(:,ii);
% if nargout>4,
% for jj = 1:ii
% D2v(:,jj,ii) = -Z*D2Yss(:,jj,ii) - Z*D2a(:,jj,ii);
% D2v(:,ii,jj) = D2v(:,jj,ii);
% end
% end
else
Dv(:,ii) = -Da(Z,ii) - DYss(Z,ii);
% if nargout>4,
% for jj = 1:ii
% D2v(:,jj,ii) = -D2Yss(Z,jj,ii) - D2a(Z,jj,ii);
% D2v(:,ii,jj) = D2v(:,jj,ii);
% end
% end
end
end
Hesst = zeros(k,k);
DLIK=zeros(k,1);
for ii = 1:k
% dai = da(:,:,ii);
dKi = DK(:,:,ii);
dtmp(:,ii) = Da(:,ii)+dKi*v+K*Dv(:,ii);
if nargout>4,
diFi = -iF*DF(:,:,ii)*iF;
for jj = 1:ii
dFj = DF(:,:,jj);
diFj = -iF*DF(:,:,jj)*iF;
dKj = DK(:,:,jj);
d2Kij = D2K(:,:,jj,ii);
d2Fij = D2F(:,:,jj,ii);
d2iFij = -diFi*dFj*iF -iF*d2Fij*iF -iF*dFj*diFi;
% dtmpj = Da(:,jj)+dKj*v+K*Dv(:,jj);
% d2vij = D2v(:,ii,jj);
if Zflag
d2vij = -Z*D2Yss(:,jj,ii) - Z*D2a(:,jj,ii);
else
d2vij = -D2Yss(Z,jj,ii) - D2a(Z,jj,ii);
end
d2tmpij = D2a(:,jj,ii) + d2Kij*v + dKj*Dv(:,ii) + dKi*Dv(:,jj) + K*d2vij;
D2a(:,jj,ii) = D2T(:,:,jj,ii)*tmp + DT(:,:,jj)*dtmp(:,ii) + DT(:,:,ii)*dtmp(:,jj) + T*d2tmpij;
D2a(:,ii,jj) = D2a(:,jj,ii);
if nargout==6,
Hesst(ii,jj) = getHesst_ij(v,Dv(:,ii),Dv(:,jj),d2vij,iF,diFi,diFj,d2iFij,dFj,d2Fij);
end
end
end
Da(:,ii) = DT(:,:,ii)*tmp + T*dtmp(:,ii);
DLIK(ii,1) = trace( iF*DF(:,:,ii) ) + 2*Dv(:,ii)'*iF*v - v'*(iF*DF(:,:,ii)*iF)*v;
end
% end of computeDLIK
function Hesst_ij = getHesst_ij(e,dei,dej,d2eij,iS,diSi,diSj,d2iSij,dSj,d2Sij);
% computes (i,j) term in the Hessian
Hesst_ij = trace(diSi*dSj + iS*d2Sij) + e'*d2iSij*e + 2*(dei'*diSj*e + dei'*iS*dej + e'*diSi*dej + e'*iS*d2eij);
% end of getHesst_ij
function [DK,DF,DP1] = computeDKalman(T,DT,DOm,P,DP,DH,Z,iF,K)
k = size(DT,3);
tmp = P-K*P(Z,:);
DF = zeros([size(iF),k]);
DK = zeros([size(K),k]);
DP1 = zeros([size(P),k]);
for ii = 1:k
DF(:,:,ii) = DP(Z,Z,ii) + DH(:,:,ii);
DiF = -iF*DF(:,:,ii)*iF;
DK(:,:,ii) = DP(:,Z,ii)*iF + P(:,Z)*DiF;
Dtmp = DP(:,:,ii) - DK(:,:,ii)*P(Z,:) - K*DP(Z,:,ii);
DP1(:,:,ii) = DT(:,:,ii)*tmp*T' + T*Dtmp*T' + T*tmp*DT(:,:,ii)' + DOm(:,:,ii);
end
% end of computeDKalman
function [DK,DF,DP1] = computeDKalmanZ(T,DT,DOm,P,DP,DH,Z,iF,K)
k = size(DT,3);
tmp = P-K*Z*P;
DF = zeros([size(iF),k]);
DK = zeros([size(K),k]);
DP1 = zeros([size(P),k]);
for ii = 1:k
DF(:,:,ii) = Z*DP(:,:,ii)*Z + DH(:,:,ii);
DiF = -iF*DF(:,:,ii)*iF;
DK(:,:,ii) = DP(:,:,ii)*Z*iF + P(:,:)*Z*DiF;
Dtmp = DP(:,:,ii) - DK(:,:,ii)*Z*P(:,:) - K*Z*DP(:,:,ii);
DP1(:,:,ii) = DT(:,:,ii)*tmp*T' + T*Dtmp*T' + T*tmp*DT(:,:,ii)' + DOm(:,:,ii);
end
% end of computeDKalmanZ
function [d2K,d2S,d2P1] = computeD2Kalman(A,dA,d2A,d2Om,P0,dP0,d2P0,DH,Z,iF,K0,dK0);
% computes the second derivatives of the Kalman matrices
% note: A=T in main func.
k = size(dA,3);
tmp = P0-K0*P0(Z,:);
[ns,no] = size(K0);
% CPC = C*P0*C'; CPC = .5*(CPC+CPC');iF = inv(CPC);
% APC = A*P0*C';
% APA = A*P0*A';
d2K = zeros(ns,no,k,k);
d2S = zeros(no,no,k,k);
d2P1 = zeros(ns,ns,k,k);
for ii = 1:k
dAi = dA(:,:,ii);
dFi = dP0(Z,Z,ii);
d2Omi = d2Om(:,:,ii);
diFi = -iF*dFi*iF;
dKi = dK0(:,:,ii);
for jj = 1:k
dAj = dA(:,:,jj);
dFj = dP0(Z,Z,jj);
d2Omj = d2Om(:,:,jj);
dFj = dP0(Z,Z,jj);
diFj = -iF*dFj*iF;
dKj = dK0(:,:,jj);
d2Aij = d2A(:,:,jj,ii);
d2Pij = d2P0(:,:,jj,ii);
d2Omij = d2Om(:,:,jj,ii);
% second order
d2Fij = d2Pij(Z,Z) ;
% d2APC = d2Aij*P0*C' + A*d2Pij*C' + A*P0*d2Cij' + dAi*dPj*C' + dAj*dPi*C' + A*dPj*dCi' + A*dPi*dCj' + dAi*P0*dCj' + dAj*P0*dCi';
d2APC = d2Pij(:,Z);
d2iF = -diFi*dFj*iF -iF*d2Fij*iF -iF*dFj*diFi;
d2Kij= d2Pij(:,Z)*iF + P0(:,Z)*d2iF + dP0(:,Z,jj)*diFi + dP0(:,Z,ii)*diFj;
d2KCP = d2Kij*P0(Z,:) + K0*d2Pij(Z,:) + dKi*dP0(Z,:,jj) + dKj*dP0(Z,:,ii) ;
dtmpi = dP0(:,:,ii) - dK0(:,:,ii)*P0(Z,:) - K0*dP0(Z,:,ii);
dtmpj = dP0(:,:,jj) - dK0(:,:,jj)*P0(Z,:) - K0*dP0(Z,:,jj);
d2tmp = d2Pij - d2KCP;
d2AtmpA = d2Aij*tmp*A' + A*d2tmp*A' + A*tmp*d2Aij' + dAi*dtmpj*A' + dAj*dtmpi*A' + A*dtmpj*dAi' + A*dtmpi*dAj' + dAi*tmp*dAj' + dAj*tmp*dAi';
d2K(:,:,ii,jj) = d2Kij; %#ok<NASGU>
d2P1(:,:,ii,jj) = d2AtmpA + d2Omij; %#ok<*NASGU>
d2S(:,:,ii,jj) = d2Fij;
% d2iS(:,:,ii,jj) = d2iF;
end
end
% end of computeD2Kalman
function [d2K,d2S,d2P1] = computeD2KalmanZ(A,dA,d2A,d2Om,P0,dP0,d2P0,DH,Z,iF,K0,dK0);
% computes the second derivatives of the Kalman matrices
% note: A=T in main func.
k = size(dA,3);
tmp = P0-K0*Z*P0(:,:);
[ns,no] = size(K0);
% CPC = C*P0*C'; CPC = .5*(CPC+CPC');iF = inv(CPC);
% APC = A*P0*C';
% APA = A*P0*A';
d2K = zeros(ns,no,k,k);
d2S = zeros(no,no,k,k);
d2P1 = zeros(ns,ns,k,k);
for ii = 1:k
dAi = dA(:,:,ii);
dFi = Z*dP0(:,:,ii)*Z;
d2Omi = d2Om(:,:,ii);
diFi = -iF*dFi*iF;
dKi = dK0(:,:,ii);
for jj = 1:k
dAj = dA(:,:,jj);
dFj = Z*dP0(:,:,jj)*Z;
d2Omj = d2Om(:,:,jj);
dFj = Z*dP0(:,:,jj)*Z;
diFj = -iF*dFj*iF;
dKj = dK0(:,:,jj);
d2Aij = d2A(:,:,jj,ii);
d2Pij = d2P0(:,:,jj,ii);
d2Omij = d2Om(:,:,jj,ii);
% second order
d2Fij = Z*d2Pij(:,:)*Z ;
% d2APC = d2Aij*P0*C' + A*d2Pij*C' + A*P0*d2Cij' + dAi*dPj*C' + dAj*dPi*C' + A*dPj*dCi' + A*dPi*dCj' + dAi*P0*dCj' + dAj*P0*dCi';
d2APC = d2Pij(:,:)*Z;
d2iF = -diFi*dFj*iF -iF*d2Fij*iF -iF*dFj*diFi;
d2Kij= d2Pij(:,:)*Z*iF + P0(:,:)*Z*d2iF + dP0(:,:,jj)*Z*diFi + dP0(:,:,ii)*Z*diFj;
d2KCP = d2Kij*Z*P0(:,:) + K0*Z*d2Pij(:,:) + dKi*Z*dP0(:,:,jj) + dKj*Z*dP0(:,:,ii) ;
dtmpi = dP0(:,:,ii) - dK0(:,:,ii)*Z*P0(:,:) - K0*Z*dP0(:,:,ii);
dtmpj = dP0(:,:,jj) - dK0(:,:,jj)*Z*P0(:,:) - K0*Z*dP0(:,:,jj);
d2tmp = d2Pij - d2KCP;
d2AtmpA = d2Aij*tmp*A' + A*d2tmp*A' + A*tmp*d2Aij' + dAi*dtmpj*A' + dAj*dtmpi*A' + A*dtmpj*dAi' + A*dtmpi*dAj' + dAi*tmp*dAj' + dAj*tmp*dAi';
d2K(:,:,ii,jj) = d2Kij; %#ok<NASGU>
d2P1(:,:,ii,jj) = d2AtmpA + d2Omij; %#ok<*NASGU>
d2S(:,:,ii,jj) = d2Fij;
% d2iS(:,:,ii,jj) = d2iF;
end
end
% end of computeD2KalmanZ

98
matlab/kalman/likelihood/kalman_filter.m
View File

@ -1,8 +1,8 @@
function [LIK, likk, a, P] = kalman_filter(Y,start,last,a,P,kalman_tol,riccati_tol,presample,T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods)
function [LIK, likk, a, P] = kalman_filter(Y,start,last,a,P,kalman_tol,riccati_tol,presample,T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods,analytic_derivation,DT,DYss,DOm,DH,DP,D2T,D2Yss,D2Om,D2H,D2P)
% Computes the likelihood of a stationnary state space model.
%@info:
%! @deftypefn {Function File} {[@var{LIK},@var{likk},@var{a},@var{P} ] =} kalman_filter (@var{Y}, @var{start}, @var{last}, @var{a}, @var{P}, @var{kalman_tol}, @var{riccati_tol},@var{presample},@var{T},@var{Q},@var{R},@var{H},@var{Z},@var{mm},@var{pp},@var{rr},@var{Zflag},@var{diffuse_periods})
%! @deftypefn {Function File} {[@var{LIK},@var{likk},@var{a},@var{P} ] =} DsgeLikelihood (@var{Y}, @var{start}, @var{last}, @var{a}, @var{P}, @var{kalman_tol}, @var{riccati_tol},@var{presample},@var{T},@var{Q},@var{R},@var{H},@var{Z},@var{mm},@var{pp},@var{rr},@var{Zflag},@var{diffuse_periods})
%! @anchor{kalman_filter}
%! @sp 1
%! Computes the likelihood of a stationary state space model, given initial condition for the states (mean and variance).
@ -63,7 +63,7 @@ function [LIK, likk, a, P] = kalman_filter(Y,start,last,a,P,kalman_tol,riccati_t
%! @sp 2
%! @strong{This function is called by:}
%! @sp 1
%! @ref{dsge_likelihood}
%! @ref{DsgeLikelihood}
%! @sp 2
%! @strong{This function calls:}
%! @sp 1
@ -93,13 +93,16 @@ function [LIK, likk, a, P] = kalman_filter(Y,start,last,a,P,kalman_tol,riccati_t
% Set defaults.
if nargin<17
Zflag = 0;
diffuse_periods = 0;
end
if nargin<18
diffuse_periods = 0;
end
if nargin<19
analytic_derivation = 0;
end
if isempty(Zflag)
Zflag = 0;
end
@ -121,6 +124,34 @@ oldK = Inf;
notsteady = 1;
F_singular = 1;
if analytic_derivation == 0,
DLIK=[];
Hess=[];
else
k = size(DT,3); % number of structural parameters
DLIK = zeros(k,1); % Initialization of the score.
Da = zeros(mm,k); % Derivative State vector.
if Zflag==0,
C = zeros(pp,mm);
for ii=1:pp; C(ii,Z(ii))=1;end % SELECTION MATRIX IN MEASUREMENT EQ. (FOR WHEN IT IS NOT CONSTANT)
else
C=Z;
end
dC = zeros(pp,mm,k); % either selection matrix or schur have zero derivatives
if analytic_derivation==2,
Hess = zeros(k,k); % Initialization of the Hessian
D2a = zeros(mm,k,k); % State vector.
d2C = zeros(pp,mm,k,k);
else
Hess=[];
D2a=[];
D2T=[];
D2Yss=[];
end
LIK={inf,DLIK,Hess};
end
while notsteady && t<=last
s = t-start+1;
if Zflag
@ -144,12 +175,27 @@ while notsteady && t<=last
likk(s) = log(dF)+transpose(v)*iF*v;
if Zflag
K = P*Z'*iF;
P = T*(P-K*Z*P)*transpose(T)+QQ;
Ptmp = T*(P-K*Z*P)*transpose(T)+QQ;
else
K = P(:,Z)*iF;
P = T*(P-K*P(Z,:))*transpose(T)+QQ;
Ptmp = T*(P-K*P(Z,:))*transpose(T)+QQ;
end
a = T*(a+K*v);
tmp = (a+K*v);
if analytic_derivation,
if analytic_derivation==2,
[Da,DP,DLIKt,D2a,D2P, Hesst] = computeDLIK(k,tmp,Z,Zflag,v,T,K,P,iF,Da,DYss,DT,DOm,DP,DH,notsteady,D2a,D2Yss,D2T,D2Om,D2P);
else
[Da,DP,DLIKt] = computeDLIK(k,tmp,Z,Zflag,v,T,K,P,iF,Da,DYss,DT,DOm,DP,DH,notsteady);
end
if t>presample
DLIK = DLIK + DLIKt;
if analytic_derivation==2,
Hess = Hess + Hesst;
end
end
end
a = T*tmp;
P=Ptmp;
notsteady = max(abs(K(:)-oldK))>riccati_tol;
oldK = K(:);
end
@ -165,12 +211,38 @@ likk(1:s) = .5*(likk(1:s) + pp*log(2*pi));
% Call steady state Kalman filter if needed.
if t<last
[tmp, likk(s+1:end)] = kalman_filter_ss(Y,t,last,a,T,K,iF,dF,Z,pp,Zflag);
if analytic_derivation,
if analytic_derivation==2,
[tmp, likk(s+1:end)] = kalman_filter_ss(Y,t,last,a,T,K,iF,dF,Z,pp,Zflag, ...
analytic_derivation,Da,DT,DYss,D2a,D2T,D2Yss);
else
[tmp, likk(s+1:end)] = kalman_filter_ss(Y,t,last,a,T,K,iF,dF,Z,pp,Zflag, ...
analytic_derivation,Da,DT,DYss);
end
DLIK = DLIK + tmp{2};
if analytic_derivation==2,
Hess = Hess + tmp{3};
end
else
[tmp, likk(s+1:end)] = kalman_filter_ss(Y,t,last,a,T,K,iF,dF,Z,pp,Zflag);
end
end
% Compute minus the log-likelihood.
if presample > diffuse_periods
LIK = sum(likk(1+presample-diffuse_periods:end));
else
LIK = sum(likk);
end
if presample
if presample>=diffuse_periods
likk = likk(1+(presample-diffuse_periods):end);
end
end
LIK = sum(likk);
if analytic_derivation,
DLIK = DLIK/2;
if analytic_derivation==2,
Hess = Hess + tril(Hess,-1)';
Hess = -Hess/2;
LIK={LIK, DLIK, Hess};
else
LIK={LIK, DLIK};
end
end

41
matlab/kalman/likelihood/kalman_filter_ss.m
View File

@ -1,4 +1,4 @@
function [LIK, likk, a] = kalman_filter_ss(Y,start,last,a,T,K,iF,dF,Z,pp,Zflag)
function [LIK, likk, a] = kalman_filter_ss(Y,start,last,a,T,K,iF,dF,Z,pp,Zflag,analytic_derivation,Da,DT,DYss,D2a,D2T,D2Yss)
% Computes the likelihood of a stationnary state space model (steady state kalman filter).
%@info:
@ -80,6 +80,23 @@ smpl = last-start+1;
t = start; % Initialization of the time index.
likk = zeros(smpl,1); % Initialization of the vector gathering the densities.
LIK = Inf; % Default value of the log likelihood.
notsteady = 0;
if nargin<12
analytic_derivation = 0;
end
if analytic_derivation == 0,
DLIK=[];
Hess=[];
else
k = size(DT,3); % number of structural parameters
DLIK = zeros(k,1); % Initialization of the score.
if analytic_derivation==2,
Hess = zeros(k,k); % Initialization of the Hessian
else
Hess=[];
end
end
while t <= last
if Zflag
@ -87,7 +104,19 @@ while t <= last
else
v = Y(:,t)-a(Z);
end
a = T*(a+K*v);
tmp = (a+K*v);
if analytic_derivation,
if analytic_derivation==2,
[Da,junk,DLIKt,D2a,junk2, Hesst] = computeDLIK(k,tmp,Z,Zflag,v,T,K,[],iF,Da,DYss,DT,[],[],[],notsteady,D2a,D2Yss,D2T,[],[]);
else
[Da,junk,DLIKt] = computeDLIK(k,tmp,Z,Zflag,v,T,K,[],iF,Da,DYss,DT,[],[],[],notsteady);
end
DLIK = DLIK + DLIKt;
if analytic_derivation==2,
Hess = Hess + Hesst;
end
end
a = T*tmp;
likk(t-start+1) = transpose(v)*iF*v;
t = t+1;
end
@ -99,4 +128,10 @@ likk = likk + log(dF);
likk = .5*(likk + pp*log(2*pi));
% Sum the observation's densities (minus the likelihood)
LIK = sum(likk);
LIK = sum(likk);
if analytic_derivation==2,
LIK={LIK,DLIK,Hess};
end
if analytic_derivation==1,
LIK={LIK,DLIK};
end

145
matlab/kalman/likelihood/univariate_computeDLIK.m Normal file
View File

@ -0,0 +1,145 @@
function [Da,DP1,DLIK,D2a,D2P,Hesst] = univariate_computeDLIK(k,indx,Z,Zflag,v,K,PZ,F,Da,DYss,DP,DH,notsteady,D2a,D2Yss,D2P)
% 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) marco.ratto@jrc.ec.europa.eu
persistent DDK DDF DD2K DD2F
if notsteady,
if Zflag
Dv = -Z*Da(:,:) - Z*DYss(:,:);
DF = zeros(k,1);
DK = zeros([rows(K),k]);
for j=1:k,
DF(j)=Z*DP(:,:,j)*Z'+DH;
DK(:,j) = (DP(:,:,j)*Z')/F-PZ*DF(j)/F^2;
end
if nargout>3
D2F = zeros(k,k);
D2v = zeros(k,k);
D2K = zeros(rows(K),k,k);
for j=1:k,
D2v(:,j) = -Z*D2a(:,:,j) - Z*D2Yss(:,:,j);
for i=j:k,
D2F(j,i)=Z*D2P(:,:,j,i)*Z';
D2F(i,j)=D2F(j,i);
D2K(:,j,i) = (D2P(:,:,j,i)*Z')/F-(DP(:,:,j)*Z')*DF(i)/F^2-(DP(:,:,i)*Z')*DF(j)/F^2- ...
PZ*D2F(j,i)/F^2 + 2*PZ/F^3*DF(i)*DF(j);
D2K(:,i,j) = D2K(:,j,i);
end
end
end
else
Dv = -Da(Z,:) - DYss(Z,:);
DF = squeeze(DP(Z,Z,:))+DH';
DK = squeeze(DP(:,Z,:))/F-PZ*transpose(DF)/F^2;
if nargout>3
D2v = squeeze(-D2a(Z,:,:) - D2Yss(Z,:,:));
D2F = squeeze(D2P(Z,Z,:,:));
D2K = squeeze(D2P(:,Z,:,:))/F;
for j=1:k,
D2K(:,:,j) = D2K(:,:,j) -PZ*D2F(j,:)/F^2 - squeeze(DP(:,Z,:))*DF(j)/F^2 - ...
squeeze(DP(:,Z,j))*DF'/F^2 + 2/F^3*PZ*DF'*DF(j);
end
end
end
if nargout>3
DD2K(:,indx,:,:)=D2K;
DD2F(indx,:,:)=D2F;
end
DDK(:,indx,:)=DK;
DDF(indx,:)=DF;
else
DK = squeeze(DDK(:,indx,:));
DF = DDF(indx,:)';
if nargout>3
D2K = squeeze(DD2K(:,indx,:,:));
D2F = squeeze(DD2F(indx,:,:));
end
if Zflag
Dv = -Z*Da(:,:) - Z*DYss(:,:);
if nargout>3
D2v = zeros(k,k);
for j=1:k,
D2v(:,j) = -Z*D2a(:,:,j) - Z*D2Yss(:,:,j);
end
end
else
Dv = -Da(Z,:) - DYss(Z,:);
if nargout>3
D2v = squeeze(-D2a(Z,:,:) - D2Yss(Z,:,:));
end
end
end
DLIK = DF/F + 2*Dv'/F*v - v^2/F^2*DF;
if nargout==6
Hesst = D2F/F-1/F^2*(DF*DF') + 2*D2v/F*v + 2*(Dv'*Dv)/F - 2*(DF*Dv)*v/F^2 ...
- v^2/F^2*D2F - 2*v/F^2*(Dv'*DF') + 2*v^2/F^3*(DF*DF');
end
Da = Da + DK*v+K*Dv;
if nargout>3
D2a = D2a + D2K*v;
for j=1:k,
% D2a(:,:,j) = D2a(:,:,j) + DK*Dv(j) + DK(:,j)*Dv + K*D2v(j,:);
for i=1:j,
D2a(:,j,i) = D2a(:,j,i) + DK(:,i)*Dv(j) + DK(:,j)*Dv(i) + K*D2v(j,i);
D2a(:,i,j) = D2a(:,j,i);
end
end
end
if notsteady,
DP1 = DP*0;
if Zflag,
for j=1:k,
DP1(:,:,j)=DP(:,:,j) - (DP(:,:,j)*Z')*K'-PZ*DK(:,j)';
end
else
for j=1:k,
DP1(:,:,j)=DP(:,:,j) - (DP(:,Z,j))*K'-PZ*DK(:,j)';
end
end
if nargout>3,
if Zflag,
for j=1:k,
D2P = D2P;
end
else
D2PZ = squeeze(D2P(:,Z,:,:));
DPZ = squeeze(DP(:,Z,:));
for j=1:k,
for i=j:k,
D2P(:,:,j,i) = D2P(:,:,j,i) - D2PZ(:,j,i)*K' - DPZ(:,j)*DK(:,i)'- DPZ(:,i)*DK(:,j)' - PZ*squeeze(D2K(:,j,i))';
D2P(:,:,i,j) = D2P(:,:,j,i);
end
end
end
end
else
DP1=DP;
end

54
matlab/kalman/likelihood/univariate_computeDstate.m Normal file
View File

@ -0,0 +1,54 @@
function [Da1,DP1,D2a,D2P] = univariate_computeDstate(k,a,P,T,Da,DP,DT,DOm,notsteady,D2a,D2P,D2T,D2Om)
% 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) marco.ratto@jrc.ec.europa.eu
DP1=DP*0;
Da1=Da*0;
for j=1:k,
Da1(:,j) = T*Da(:,j) + DT(:,:,j)*a;
if notsteady,
DP1(:,:,j) = T*DP(:,:,j)*T'+DT(:,:,j)*P*T'+T*P*DT(:,:,j)';
else
DP1=DP;
end
end
if notsteady,
DP1 = DP1 + DOm;
end
if nargout>2,
for j=1:k,
for i=1:j,
D2a(:,j,i) = DT(:,:,i)*Da(:,j) + DT(:,:,j)*Da(:,i) + T*D2a(:,j,i)+ D2T(:,:,j,i)*a;
D2a(:,i,j) = D2a(:,j,i);
if notsteady,
D2P(:,:,j,i) = T*D2P(:,:,j,i)*T' +DT(:,:,i)*DP(:,:,j)*T'+T*DP(:,:,j)*DT(:,:,i)' + ...
DT(:,:,j)*DP(:,:,i)*T'+T*DP(:,:,i)*DT(:,:,j)' + ...
DT(:,:,j)*P*DT(:,:,i)'+DT(:,:,i)*P*DT(:,:,j)'+ ...
D2T(:,:,j,i)*P*T'+T*P*D2T(:,:,j,i)';
D2P(:,:,i,j) = D2P(:,:,j,i);
end
end
end
if notsteady,
D2P = D2P + D2Om;
end
end

78
matlab/kalman/likelihood/univariate_kalman_filter.m
View File

@ -120,6 +120,34 @@ notsteady = 1;
oldK = Inf;
K = NaN(mm,pp);
if analytic_derivation == 0,
DLIK=[];
Hess=[];
else
k = size(DT,3); % number of structural parameters
DLIK = zeros(k,1); % Initialization of the score.
Da = zeros(mm,k); % Derivative State vector.
if Zflag==0,
C = zeros(pp,mm);
for ii=1:pp; C(ii,Z(ii))=1;end % SELECTION MATRIX IN MEASUREMENT EQ. (FOR WHEN IT IS NOT CONSTANT)
else
C=Z;
end
dC = zeros(pp,mm,k); % either selection matrix or schur have zero derivatives
if analytic_derivation==2,
Hess = zeros(k,k); % Initialization of the Hessian
D2a = zeros(mm,k,k); % State vector.
d2C = zeros(pp,mm,k,k);
else
Hess=[];
D2a=[];
D2T=[];
D2Yss=[];
end
LIK={inf,DLIK,Hess};
end
while notsteady && t<=last
s = t-start+1;
d_index = data_index{t};
@ -144,9 +172,29 @@ while notsteady && t<=last
if t>=no_more_missing_observations
K(:,i) = Ki;
end
lik(s) = lik(s) + log(Fi) + prediction_error*prediction_error/Fi + l2pi;
if analytic_derivation,
if analytic_derivation==2,
[Da,DP,DLIKt,D2a,D2P, Hesst] = univariate_computeDLIK(k,i,z(i,:),Zflag,prediction_error,Ki,PZ,Fi,Da,DYss,DP,DH(d_index(i),:),notsteady,D2a,D2Yss,D2P);
else
[Da,DP,DLIKt] = univariate_computeDLIK(k,i,z(i,:),Zflag,prediction_error,Ki,PZ,Fi,Da,DYss,DP,DH(d_index(i),:),notsteady);
end
if t>presample
DLIK = DLIK + DLIKt;
if analytic_derivation==2,
Hess = Hess + Hesst;
end
end
end
a = a + Ki*prediction_error;
P = P - PZ*Ki';
lik(s) = lik(s) + log(Fi) + prediction_error*prediction_error/Fi + l2pi;
end
end
if analytic_derivation,
if analytic_derivation==2,
[Da,DP,D2a,D2P] = univariate_computeDstate(k,a,P,T,Da,DP,DT,DOm,notsteady,D2a,D2P,D2T,D2Om);
else
[Da,DP] = univariate_computeDstate(k,a,P,T,Da,DP,DT,DOm,notsteady);
end
end
a = T*a;
@ -163,7 +211,21 @@ lik(1:s) = .5*lik(1:s);
% Call steady state univariate kalman filter if needed.
if t<last
[tmp, lik(s+1:end)] = univariate_kalman_filter_ss(Y,t,last,a,P,kalman_tol,T,H,Z,pp,Zflag);
if analytic_derivation,
if analytic_derivation==2,
[tmp, lik(s+1:end)] = univariate_kalman_filter_ss(Y,t,last,a,P,kalman_tol,T,H,Z,pp,Zflag, ...
analytic_derivation,Da,DT,DYss,DP,DH,D2a,D2T,D2Yss,D2P);
else
[tmp, lik(s+1:end)] = univariate_kalman_filter_ss(Y,t,last,a,P,kalman_tol,T,H,Z,pp,Zflag, ...
analytic_derivation,Da,DT,DYss,DP,DH);
end
DLIK = DLIK + tmp{2};
if analytic_derivation==2,
Hess = Hess + tmp{3};
end
else
[tmp, lik(s+1:end)] = univariate_kalman_filter_ss(Y,t,last,a,P,kalman_tol,T,H,Z,pp,Zflag);
end
end
% Compute minus the log-likelihood.
@ -171,4 +233,14 @@ if presample > diffuse_periods
LIK = sum(lik(1+presample-diffuse_periods:end));
else
LIK = sum(lik);
end
end
if analytic_derivation,
DLIK = DLIK/2;
if analytic_derivation==2,
Hess = -Hess/2;
LIK={LIK, DLIK, Hess};
else
LIK={LIK, DLIK};
end
end

51
matlab/kalman/likelihood/univariate_kalman_filter_ss.m
View File

@ -1,4 +1,4 @@
function [LIK,likk,a] = univariate_kalman_filter_ss(Y,start,last,a,P,kalman_tol,T,H,Z,pp,Zflag)
function [LIK,likk,a] = univariate_kalman_filter_ss(Y,start,last,a,P,kalman_tol,T,H,Z,pp,Zflag,analytic_derivation,Da,DT,DYss,DP,DH,D2a,D2T,D2Yss,D2P)
% Computes the likelihood of a stationnary state space model (steady state univariate kalman filter).
%@info:
@ -83,10 +83,33 @@ likk = zeros(smpl,1); % Initialization of the vector gathering the densitie
LIK = Inf; % Default value of the log likelihood.
l2pi = log(2*pi);
if nargin<12
analytic_derivation = 0;
end
if analytic_derivation == 0,
DLIK=[];
Hess=[];
else
k = size(DT,3); % number of structural parameters
DLIK = zeros(k,1); % Initialization of the score.
if analytic_derivation==2,
Hess = zeros(k,k); % Initialization of the Hessian
else
Hess=[];
end
end
% Steady state kalman filter.
while t<=last
s = t-start+1;
PP = P;
if analytic_derivation,
DPP = DP;
if analytic_derivation==2,
D2PP = D2P;
end
end
for i=1:pp
if Zflag
prediction_error = Y(i,t) - Z(i,:)*a;
@ -102,6 +125,24 @@ while t<=last
a = a + Ki*prediction_error;
PP = PP - PPZ*Ki';
likk(s) = likk(s) + log(Fi) + prediction_error*prediction_error/Fi + l2pi;
if analytic_derivation,
if analytic_derivation==2,
[Da,DPP,DLIKt,D2a,D2PP, Hesst] = univariate_computeDLIK(k,i,Z(i,:),Zflag,prediction_error,Ki,PPZ,Fi,Da,DYss,DPP,DH(i,:),0,D2a,D2Yss,D2PP);
else
[Da,DPP,DLIKt] = univariate_computeDLIK(k,i,Z(i,:),Zflag,prediction_error,Ki,PPZ,Fi,Da,DYss,DPP,DH(i,:),0);
end
DLIK = DLIK + DLIKt;
if analytic_derivation==2,
Hess = Hess + Hesst;
end
end
end
end
if analytic_derivation,
if analytic_derivation==2,
[Da,junk,D2a] = univariate_computeDstate(k,a,P,T,Da,DP,DT,[],0,D2a,D2P,D2T);
else
Da = univariate_computeDstate(k,a,P,T,Da,DP,DT,[],0);
end
end
a = T*a;
@ -110,4 +151,10 @@ end
likk = .5*likk;
LIK = sum(likk);
LIK = sum(likk);
if analytic_derivation==2,
LIK={LIK,DLIK,Hess};
end
if analytic_derivation==1,
LIK={LIK,DLIK};
end

12
matlab/moment_function.m
View File

@ -1,4 +1,4 @@
function [g,flag] = moment_function(xparams,sample_moments,dataset,options,parallel)
function [g,grad,hess,flag] = moment_function(xparams,sample_moments,dataset,options,parallel)
% Evaluates the moment function of the Simulated Moments Method (discrepancy between sample and
% ).
%
@ -15,7 +15,7 @@ function [g,flag] = moment_function(xparams,sample_moments,dataset,options,paral
% SPECIAL REQUIREMENTS
% The user has to provide a file where the moment conditions are defined.
% Copyright (C) 2010-2012 Dynare Team
% Copyright (C) 2010 Dynare Team
%
% This file is part of Dynare.
%
@ -37,14 +37,12 @@ persistent mainStream mainState
persistent priorObjectiveValue
flag = 1;
grad=[];
hess=[];
if nargin<5
if isempty(mainStream)
if matlab_ver_less_than('7.12')
mainStream = RandStream.getDefaultStream;
else
mainStream = RandStream.getGlobalStream;
end
mainStream = RandStream.getDefaultStream;
mainState = mainStream.State;
else
mainStream.State = mainState;

4
matlab/numgrad2.m
View File

@ -39,11 +39,11 @@ for i=1:n
else
tvecv=tvec(:,i);
end
[fh,cost_flag] = feval(fcn, x+scale*transpose(tvecv), varargin{:});
[fh,junk1,junk2,cost_flag] = feval(fcn, x+scale*transpose(tvecv), varargin{:});
if cost_flag
g0 = (fh - f0) / (scale*delta);
else
[fh,cost_flag] = feval(fcn, x-scale*transpose(tvecv), varargin{:});
[fh,junk1,junk2,cost_flag] = feval(fcn, x-scale*transpose(tvecv), varargin{:});
if cost_flag
g0 = (f0-fh) / (scale*delta);
else

4
matlab/numgrad3.m
View File

@ -45,8 +45,8 @@ for i=1:n
else
tvecv=tvec(:,i);
end
[f1,cost_flag1] = feval(fcn, x+scale*transpose(tvecv), varargin{:});
[f2,cost_flag2] = feval(fcn, x-scale*transpose(tvecv), varargin{:});
[f1,junk1,junk2,cost_flag1] = feval(fcn, x+scale*transpose(tvecv), varargin{:});
[f2,junk1,junk2,cost_flag2] = feval(fcn, x-scale*transpose(tvecv), varargin{:});
if cost_flag1 && cost_flag2
g0 = (f1 - f2) / (2*scale*delta);
else

8
matlab/numgrad5.m
View File

@ -50,15 +50,15 @@ for i=1:n
else
tvecv=tvec(:,i);
end
[f1,cost_flag1] = feval(fcn, x+scale*transpose(tvecv), varargin{:});
[f2,cost_flag2] = feval(fcn, x-scale*transpose(tvecv), varargin{:});
[f1,junk1,junk2,cost_flag1] = feval(fcn, x+scale*transpose(tvecv), varargin{:});
[f2,junk1,junk2,cost_flag2] = feval(fcn, x-scale*transpose(tvecv), varargin{:});
if cost_flag1==0 || cost_flag2==0
cost_flag3 = 0;
cost_flag4 = 0;
disp('numgrad:: I cannot use the five points formula!!')
else
[f3,cost_flag3] = feval(fcn, x+2*scale*transpose(tvecv), varargin{:});
[f4,cost_flag4] = feval(fcn, x-2*scale*transpose(tvecv), varargin{:});
[f3,junk1,junk2,cost_flag3] = feval(fcn, x+2*scale*transpose(tvecv), varargin{:});
[f4,junk1,junk2,cost_flag4] = feval(fcn, x-2*scale*transpose(tvecv), varargin{:});
end
if cost_flag1 && cost_flag2 && cost_flag3 && cost_flag4% Five Points formula
g0 = (8*(f1 - f2)+ f4-f3) / (12*scale*delta);

8
matlab/simplex_optimization_routine.m
View File

@ -151,6 +151,7 @@ else
delta = 0.05;
end
DELTA = delta;
zero_delta = delta/200;% To be used instead of delta if x(i) is zero.
% Set max_no_improvements.
if isfield(options,'max_no_improvements')
@ -173,7 +174,7 @@ if verbose
disp(' ')
end
initial_point = x;
[initial_score,nopenalty] = feval(objective_function,x,varargin{:});
[initial_score,junk1,junk2,nopenalty] = feval(objective_function,x,varargin{:});
if ~nopenalty
error('simplex_optimization_routine:: Initial condition is wrong!')
else
@ -509,7 +510,6 @@ function [v,fv,delta] = simplex_initialization(objective_function,point,point_sc
v(:,1) = point;
fv = zeros(n+1,1);
fv(1) = point_score;
zero_delta = delta/200;% To be used instead of delta if x(i) is zero.
if length(delta)==1
delta = repmat(delta,n,1);
end
@ -522,7 +522,7 @@ function [v,fv,delta] = simplex_initialization(objective_function,point,point_sc
end
v(:,j+1) = y;
x = y;
[fv(j+1),nopenalty_flag] = feval(objective_function,x,varargin{:});
[fv(j+1),junk1,junk2,nopenalty_flag] = feval(objective_function,x,varargin{:});
if check_delta
while ~nopenalty_flag
if y(j)~=0
@ -538,7 +538,7 @@ function [v,fv,delta] = simplex_initialization(objective_function,point,point_sc
end
v(:,j+1) = y;
x = y;
[fv(j+1),nopenalty_flag] = feval(objective_function,x,varargin{:});
[fv(j+1),junk1,junk2,nopenalty_flag] = feval(objective_function,x,varargin{:});
end
end
end

69
tests/analytic_derivatives/ls2003.mod Normal file
View File

@ -0,0 +1,69 @@
var y y_s R pie dq pie_s de A y_obs pie_obs R_obs;
varexo e_R e_q e_ys e_pies e_A;
parameters psi1 psi2 psi3 rho_R tau alpha rr k rho_q rho_A rho_ys rho_pies;
psi1 = 1.54;
psi2 = 0.25;
psi3 = 0.25;
rho_R = 0.5;
alpha = 0.3;
rr = 2.51;
k = 0.5;
tau = 0.5;
rho_q = 0.4;
rho_A = 0.2;
rho_ys = 0.9;
rho_pies = 0.7;
model(linear);
y = y(+1) - (tau +alpha*(2-alpha)*(1-tau))*(R-pie(+1))-alpha*(tau +alpha*(2-alpha)*(1-tau))*dq(+1) + alpha*(2-alpha)*((1-tau)/tau)*(y_s-y_s(+1))-A(+1);
pie = exp(-rr/400)*pie(+1)+alpha*exp(-rr/400)*dq(+1)-alpha*dq+(k/(tau+alpha*(2-alpha)*(1-tau)))*y+k*alpha*(2-alpha)*(1-tau)/(tau*(tau+alpha*(2-alpha)*(1-tau)))*y_s;
pie = de+(1-alpha)*dq+pie_s;
R = rho_R*R(-1)+(1-rho_R)*(psi1*pie+psi2*(y+alpha*(2-alpha)*((1-tau)/tau)*y_s)+psi3*de)+e_R;
dq = rho_q*dq(-1)+e_q;
y_s = rho_ys*y_s(-1)+e_ys;
pie_s = rho_pies*pie_s(-1)+e_pies;
A = rho_A*A(-1)+e_A;
y_obs = y-y(-1)+A;
pie_obs = 4*pie;
R_obs = 4*R;
end;
shocks;
var e_R = 1.25^2;
var e_q = 2.5^2;
var e_A = 1.89;
var e_ys = 1.89;
var e_pies = 1.89;
end;
varobs y_obs R_obs pie_obs dq de;
estimated_params;
psi1 , gamma_pdf,1.5,0.5;
psi2 , gamma_pdf,0.25,0.125;
psi3 , gamma_pdf,0.25,0.125;
rho_R ,beta_pdf,0.5,0.2;
alpha ,beta_pdf,0.3,0.1;
rr ,gamma_pdf,2.5,1;
k , gamma_pdf,0.5,0.25;
tau ,gamma_pdf,0.5,0.2;
rho_q ,beta_pdf,0.4,0.2;
rho_A ,beta_pdf,0.5,0.2;
rho_ys ,beta_pdf,0.8,0.1;
rho_pies,beta_pdf,0.7,0.15;
stderr e_R,inv_gamma_pdf,1.2533,0.6551;
stderr e_q,inv_gamma_pdf,2.5066,1.3103;
stderr e_A,inv_gamma_pdf,1.2533,0.6551;
stderr e_ys,inv_gamma_pdf,1.2533,0.6551;
stderr e_pies,inv_gamma_pdf,1.88,0.9827;
end;
options_.analytic_derivation=1;
estimation(datafile=data_ca1,first_obs=8,nobs=79,mh_nblocks=2,
prefilter=1,mh_jscale=0.5,mh_replic=0, mode_compute=1);
identification;