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dsge_likelihood.m
Marco Ratto authored
1) allow to compute derivatives starting from NUMERICAL derivatives of jacobian and steady state: this has a minor cost in accuracy and allow apply without errors identification and estimation with numerical derivatives; 2) added trap in dynare_estimation_init: if steadystate changes param values, automaticly shifts to numerical derivs of jacoban and steady state + analytic derivatives of all the rest; 3) bug fixes for 2nd order derivatives w.r.t. model parameters;
dsge_likelihood.m 29.08 KiB
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:
%! @deftypefn {Function File} {[@var{fval},@var{exit_flag},@var{ys},@var{trend_coeff},@var{info},@var{Model},@var{DynareOptions},@var{BayesInfo},@var{DynareResults},@var{DLIK},@var{AHess}] =} dsge_likelihood (@var{xparam1},@var{DynareDataset},@var{DynareOptions},@var{Model},@var{EstimatedParameters},@var{BayesInfo},@var{DynareResults},@var{derivatives_flag})
%! @anchor{dsge_likelihood}
%! @sp 1
%! Evaluates the posterior kernel of a dsge model.
%! @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_}).
%! @item derivates_flag
%! Integer scalar, flag for analytical derivatives of the likelihood.
%! @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==46
%! Likelihood is a complex valued number.
%! @item info==47
%! Posterior kernel is not a number (logged prior density is NaN)
%! @item info==48
%! Posterior kernel is a complex valued number (logged prior density is complex).
%! @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_}).
%! @item DLIK
%! Vector of doubles, score of the likelihood.
%! @item AHess
%! Matrix of doubles, asymptotic hessian matrix.
%! @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{schur_statespace_transformation}, @ref{kalman_filter_d}, @ref{missing_observations_kalman_filter_d}, @ref{univariate_kalman_filter_d}, @ref{kalman_steady_state}, @ref{getH}, @ref{kalman_filter}, @ref{score}, @ref{AHessian}, @ref{missing_observations_kalman_filter}, @ref{univariate_kalman_filter}, @ref{priordens}
%! @end deftypefn
%@eod:
% Copyright (C) 2004-2012 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
% Declaration of the penalty as a persistent variable.
% Persistent variable 'penalty' is used to compute an endogenous penalty to
% the value 'fval' when various conditions are encountered. These conditions
% set also 'exit_flag' equal to 0 instead of 1. It is only when
% dsge_likelihood() is called by an optimizer called by
% dynare_estimation_1() that 'exit_flag' is ignored and penalized 'fval' is
% actually used.% In that case, 'penalty' is properly initialized, at the very end of the
% present function, by a call to dsge_likelihood() made in
% initial_estimation_checks(). If a condition triggers exit_flag ==
% 0, initial_estimation_checks() triggers an error.
% In summary, an initial call to the present function, without triggering
% any condition, guarantees that 'penalty' is properly initialized when needed.
persistent penalty
% Initialization of the returned variables and others...
fval = [];
ys = [];
trend_coeff = [];
exit_flag = 1;
info = 0;
singularity_flag = 0;
DLIK = [];
Hess = [];
if DynareOptions.estimation_dll
[fval,exit_flag,ys,trend_coeff,info,params,H,Q] ...
= logposterior(xparam1,DynareDataset, DynareOptions,Model, ...
EstimatedParameters,BayesInfo,DynareResults);
Model.params = params;
if ~isequal(Model.H,0)
Model.H = H;
end
Model.Sigma_e = Q;
DynareResults.dr.ys = ys;
return
end
% Set flag related to analytical derivatives.
analytic_derivation = DynareOptions.analytic_derivation;
if analytic_derivation && DynareOptions.loglinear
error('The analytic_derivation and loglinear options are not compatible')
end
if nargout==1,
analytic_derivation=0;
end
if analytic_derivation,
kron_flag=DynareOptions.analytic_derivation_mode;
end
%------------------------------------------------------------------------------
% 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 ~isequal(DynareOptions.mode_compute,1) && any(xparam1<BayesInfo.lb)
k = find(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
% Return, with endogenous penalty, if some parameters are greater than the upper bound of the prior domain.
if ~isequal(DynareOptions.mode_compute,1) && any(xparam1>BayesInfo.ub)
k = find(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
% Get the diagonal elements of the covariance matrices for the structural innovations (Q) and the measurement error (H).
Model = set_all_parameters(xparam1,EstimatedParameters,Model);
Q = Model.Sigma_e;
H = Model.H;
% Test if Q is positive definite.
if EstimatedParameters.ncx
% 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 = penalty+sum(-a(k));
exit_flag = 0;
info = 43;
return
end
end
end
% Test if H is positive definite.
if EstimatedParameters.ncn
% 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 = penalty+sum(-a(k));
exit_flag = 0;
info = 44;
return
end
end
end
%------------------------------------------------------------------------------
% 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');
% Return, with endogenous penalty when possible, if dynare_resolve issues an error code (defined in resol).
if info(1) == 1 || info(1) == 2 || info(1) == 5 || info(1) == 7 || info(1) == 22 || info(1) == 24
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
returnend
% Define a vector of indices for the observed variables. Is this really usefull?...
BayesInfo.mf = BayesInfo.mf1;
% Define the constant vector of the measurement equation.
if DynareOptions.noconstant
constant = zeros(DynareDataset.info.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;
Z = BayesInfo.mf; % old mf
no_missing_data_flag = ~DynareDataset.missing.state;
mm = length(T); % old np
pp = DynareDataset.info.nvobs;
rr = length(Q);
kalman_tol = DynareOptions.kalman_tol;
riccati_tol = DynareOptions.riccati_tol;
Y = DynareDataset.data-trend;
%------------------------------------------------------------------------------
% 3. Initial condition of the Kalman filter
%------------------------------------------------------------------------------
kalman_algo = DynareOptions.kalman_algo;
% resetting measurement errors covariance matrix for univariate filters
if (kalman_algo == 2) || (kalman_algo == 4)
if isequal(H,0)
H = zeros(pp,1);
mmm = mm;
else
if all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
H = diag(H);
mmm = mm;
else
Z = [Z, eye(pp)];
T = blkdiag(T,zeros(pp));
Q = blkdiag(Q,H);
R = blkdiag(R,eye(pp));
Pstar = blkdiag(Pstar,H);
Pinf = blckdiag(Pinf,zeros(pp));
H = zeros(pp,1);
mmm = mm+pp;
end
end
end
diffuse_periods = 0;correlated_errors_have_been_checked = 0;
singular_diffuse_filter = 0;
switch DynareOptions.lik_init
case 1% Standard initialization with the steady state of the state equation.
if kalman_algo~=2
% Use standard kalman filter except if the univariate filter is explicitely choosen.
kalman_algo = 1;
end
if DynareOptions.lyapunov_fp == 1
Pstar = lyapunov_symm(T,Q,DynareOptions.lyapunov_fixed_point_tol,DynareOptions.lyapunov_complex_threshold, 3, R);
elseif DynareOptions.lyapunov_db == 1
Pstar = disclyap_fast(T,R*Q*R',DynareOptions.lyapunov_doubling_tol);
elseif DynareOptions.lyapunov_srs == 1
Pstar = lyapunov_symm(T,Q,DynareOptions.lyapunov_fixed_point_tol,DynareOptions.lyapunov_complex_threshold, 4, R);
else
Pstar = lyapunov_symm(T,R*Q*R',DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold);
end;
Pinf = [];
a = zeros(mm,1);
Zflag = 0;
case 2% Initialization with large numbers on the diagonal of the covariance matrix if the states (for non stationary models).
if kalman_algo ~= 2
% Use standard kalman filter except if the univariate filter is explicitely choosen.
kalman_algo = 1;
end
Pstar = DynareOptions.Harvey_scale_factor*eye(mm);
Pinf = [];
a = zeros(mm,1);
Zflag = 0;
case 3% Diffuse Kalman filter (Durbin and Koopman)
% Use standard kalman filter except if the univariate filter is explicitely choosen.
if kalman_algo == 0
kalman_algo = 3;
elseif ~((kalman_algo == 3) || (kalman_algo == 4))
error(['diffuse filter: options_.kalman_algo can only be equal ' ...
'to 0 (default), 3 or 4'])
end
[Z,T,R,QT,Pstar,Pinf] = schur_statespace_transformation(Z,T,R,Q,DynareOptions.qz_criterium);
Zflag = 1;
% Run diffuse kalman filter on first periods.
if (kalman_algo==3)
% Multivariate Diffuse Kalman Filter
if no_missing_data_flag
[dLIK,dlik,a,Pstar] = kalman_filter_d(Y, 1, size(Y,2), ...
zeros(mm,1), Pinf, Pstar, ...
kalman_tol, riccati_tol, DynareOptions.presample, ...
T,R,Q,H,Z,mm,pp,rr);
else
[dLIK,dlik,a,Pstar] = missing_observations_kalman_filter_d(DynareDataset.missing.aindex,DynareDataset.missing.number_of_observations,DynareDataset.missing.no_more_missing_observations, ...
Y, 1, size(Y,2), ...
zeros(mm,1), Pinf, Pstar, ...
kalman_tol, riccati_tol, DynareOptions.presample, ...
T,R,Q,H,Z,mm,pp,rr);
end
diffuse_periods = length(dlik);
if isinf(dLIK)
% Go to univariate diffuse filter if singularity problem.
singular_diffuse_filter = 1;
end
end
if singular_diffuse_filter || (kalman_algo==4)
% Univariate Diffuse Kalman Filter
if isequal(H,0)
H1 = zeros(pp,1);
mmm = mm;
else
if all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
H1 = diag(H);
mmm = mm; else
Z = [Z, eye(pp)];
T = blkdiag(T,zeros(pp));
Q = blkdiag(Q,H);
R = blkdiag(R,eye(pp));
Pstar = blkdiag(Pstar,H);
Pinf = blckdiag(Pinf,zeros(pp));
H1 = zeros(pp,1);
mmm = mm+pp;
end
end
% no need to test again for correlation elements
correlated_errors_have_been_checked = 1;
[dLIK,dlik,a,Pstar] = univariate_kalman_filter_d(DynareDataset.missing.aindex,...
DynareDataset.missing.number_of_observations,...
DynareDataset.missing.no_more_missing_observations, ...
Y, 1, size(Y,2), ...
zeros(mmm,1), Pinf, Pstar, ...
kalman_tol, riccati_tol, DynareOptions.presample, ...
T,R,Q,H1,Z,mmm,pp,rr);
diffuse_periods = length(dlik);
end
case 4% Start from the solution of the Riccati equation.
if kalman_algo ~= 2
kalman_algo = 1;
end
if isequal(H,0)
[err,Pstar] = kalman_steady_state(transpose(T),R*Q*transpose(R),transpose(build_selection_matrix(Z,mm,length(Z))));
else
[err,Pstar] = kalman_steady_state(transpose(T),R*Q*transpose(R),transpose(build_selection_matrix(Z,mm,length(Z))),H);
end
if err
disp(['dsge_likelihood:: I am not able to solve the Riccati equation, so I switch to lik_init=1!']);
DynareOptions.lik_init = 1;
Pstar = lyapunov_symm(T,R*Q*R',DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold);
end
Pinf = [];
a = zeros(mm,1);
Zflag = 0;
otherwise
error('dsge_likelihood:: Unknown initialization approach for the Kalman filter!')
end
if analytic_derivation,
offset = EstimatedParameters.nvx;
offset = offset+EstimatedParameters.nvn;
offset = offset+EstimatedParameters.ncx;
offset = offset+EstimatedParameters.ncn;
no_DLIK = 0;
full_Hess = analytic_derivation==2;
asy_Hess = analytic_derivation==-2;
outer_product_gradient = analytic_derivation==-1;
if asy_Hess,
analytic_derivation=1;
end
if outer_product_gradient,
analytic_derivation=1;
end
DLIK = [];
AHess = [];
if nargin<8 || isempty(derivatives_info)
[A,B,nou,nou,Model,DynareOptions,DynareResults] = dynare_resolve(Model,DynareOptions,DynareResults);
if ~isempty(EstimatedParameters.var_exo)
indexo=EstimatedParameters.var_exo(:,1);
else
indexo=[];
end
if ~isempty(EstimatedParameters.param_vals) indparam=EstimatedParameters.param_vals(:,1);
else
indparam=[];
end
if full_Hess,
[dum, DT, DOm, DYss, dum2, D2T, D2Om, D2Yss] = getH(A, B, Model,DynareResults,DynareOptions,kron_flag,indparam,indexo);
else
[dum, DT, DOm, DYss] = getH(A, B, Model,DynareResults,DynareOptions,kron_flag,indparam,indexo);
end
else
DT = derivatives_info.DT;
DOm = derivatives_info.DOm;
DYss = derivatives_info.DYss;
if isfield(derivatives_info,'full_Hess'),
full_Hess = derivatives_info.full_Hess;
end
if full_Hess,
D2T = derivatives_info.D2T;
D2Om = derivatives_info.D2Om;
D2Yss = derivatives_info.D2Yss;
end
if isfield(derivatives_info,'no_DLIK'),
no_DLIK = derivatives_info.no_DLIK;
end
clear('derivatives_info');
end
iv = DynareResults.dr.restrict_var_list;
DYss = [zeros(size(DYss,1),offset) DYss];
DT = DT(iv,iv,:);
DOm = DOm(iv,iv,:);
DYss = DYss(iv,:);
DH=zeros([length(H),length(H),length(xparam1)]);
DQ=zeros([size(Q),length(xparam1)]);
DP=zeros([size(T),length(xparam1)]);
if full_Hess,
for j=1:size(D2Yss,1),
tmp(j,:,:) = blkdiag(zeros(offset,offset), squeeze(D2Yss(j,:,:)));
end
D2Yss = tmp;
D2T = D2T(iv,iv,:,:);
D2Om = D2Om(iv,iv,:,:);
D2Yss = D2Yss(iv,:,:);
D2H=zeros([size(H),length(xparam1),length(xparam1)]);
D2P=zeros([size(T),length(xparam1),length(xparam1)]);
end
for i=1:EstimatedParameters.nvx
k =EstimatedParameters.var_exo(i,1);
DQ(k,k,i) = 2*sqrt(Q(k,k));
dum = lyapunov_symm(T,DOm(:,:,i),DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold);
kk = find(abs(dum) < 1e-12);
dum(kk) = 0;
DP(:,:,i)=dum;
if full_Hess
for j=1:i,
dum = lyapunov_symm(T,D2Om(:,:,i,j),DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold);
kk = (abs(dum) < 1e-12);
dum(kk) = 0;
D2P(:,:,i,j)=dum;
D2P(:,:,j,i)=dum;
end
end
end
offset = EstimatedParameters.nvx;
for i=1:EstimatedParameters.nvn
k = EstimatedParameters.var_endo(i,1);
DH(k,k,i+offset) = 2*sqrt(H(k,k));
if full_Hess
D2H(k,k,i+offset,i+offset) = 2;
end end
offset = offset + EstimatedParameters.nvn;
for j=1:EstimatedParameters.np
dum = lyapunov_symm(T,DT(:,:,j+offset)*Pstar*T'+T*Pstar*DT(:,:,j+offset)'+DOm(:,:,j+offset),DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold);
kk = find(abs(dum) < 1e-12);
dum(kk) = 0;
DP(:,:,j+offset)=dum;
if full_Hess
DTj = DT(:,:,j+offset);
DPj = dum;
for i=1:j,
DTi = DT(:,:,i+offset);
DPi = DP(:,:,i+offset);
D2Tij = D2T(:,:,i,j);
D2Omij = D2Om(:,:,i,j);
tmp = D2Tij*Pstar*T' + T*Pstar*D2Tij' + DTi*DPj*T' + DTj*DPi*T' + T*DPj*DTi' + T*DPi*DTj' + DTi*Pstar*DTj' + DTj*Pstar*DTi' + D2Omij;
dum = lyapunov_symm(T,tmp,DynareOptions.qz_criterium,DynareOptions.lyapunov_complex_threshold);
dum(abs(dum)<1.e-12) = 0;
D2P(:,:,i+offset,j+offset) = dum;
D2P(:,:,j+offset,i+offset) = dum;
end
end
end
if analytic_derivation==1,
analytic_deriv_info={analytic_derivation,DT,DYss,DOm,DH,DP,asy_Hess};
else
analytic_deriv_info={analytic_derivation,DT,DYss,DOm,DH,DP,D2T,D2Yss,D2Om,D2H,D2P};
end
else
analytic_deriv_info={0};
end
%------------------------------------------------------------------------------
% 4. Likelihood evaluation
%------------------------------------------------------------------------------
if ((kalman_algo==1) || (kalman_algo==3))% Multivariate Kalman Filter
if no_missing_data_flag
if DynareOptions.block
[err, LIK] = block_kalman_filter(T,R,Q,H,Pstar,Y,start,Z,kalman_tol,riccati_tol, Model.nz_state_var, Model.n_diag, Model.nobs_non_statevar);
mexErrCheck('block_kalman_filter', err);
else
[LIK,lik] = kalman_filter(Y,diffuse_periods+1,size(Y,2), ...
a,Pstar, ...
kalman_tol, riccati_tol, ...
DynareOptions.presample, ...
T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods, ...
analytic_deriv_info{:});
end
else
if 0 %DynareOptions.block
[err, LIK,lik] = block_kalman_filter(DynareDataset.missing.aindex,DynareDataset.missing.number_of_observations,DynareDataset.missing.no_more_missing_observations,...
T,R,Q,H,Pstar,Y,start,Z,kalman_tol,riccati_tol, Model.nz_state_var, Model.n_diag, Model.nobs_non_statevar);
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), ...
a, Pstar, ...
kalman_tol, DynareOptions.riccati_tol, ...
DynareOptions.presample, ...
T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods);
end;
end
if analytic_derivation,
LIK1=LIK;
LIK=LIK1{1};
lik1=lik;
lik=lik1{1};
end
if isinf(LIK)
if kalman_algo == 1 kalman_algo = 2;
else
kalman_algo = 4;
end
else
if DynareOptions.lik_init==3
LIK = LIK + dLIK;
if analytic_derivation==0 && nargout==2,
lik = [dlik; lik];
end
end
end
end
if (kalman_algo==2) || (kalman_algo==4)
% Univariate Kalman Filter
% resetting measurement error covariance matrix when necessary %
if ~correlated_errors_have_been_checked
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;
clear tmp
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));
Q = blkdiag(Q,H);
R = blkdiag(R,eye(pp));
Pstar = blkdiag(Pstar,H);
Pinf = blckdiag(Pinf,zeros(pp));
H = zeros(pp,1);
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), ...
a,Pstar, ...
DynareOptions.kalman_tol, ...
DynareOptions.riccati_tol, ...
DynareOptions.presample, ...
T,Q,R,H,Z,mmm,pp,rr,Zflag,diffuse_periods,analytic_deriv_info{:});
if analytic_derivation,
LIK1=LIK;
LIK=LIK1{1};
lik1=lik;
lik=lik1{1};
end
if DynareOptions.lik_init==3
LIK = LIK+dLIK;
if analytic_derivation==0 && nargout==2,
lik = [dlik; lik];
end
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,
% if ~((kalman_algo==2) || (kalman_algo==4)),
% [Hess] = AHessian(T,R,Q,H,Pstar,Y,DT,DYss,DOm,DH,DP,start,Z,kalman_tol,riccati_tol);
% else
Hess = LIK1{3};
% end
end
end
if isnan(LIK)
info = 45;
exit_flag = 0;
return
end
if imag(LIK)~=0
info = 46;
exit_flag = 0;
return
end
likelihood = LIK;
% ------------------------------------------------------------------------------
% 5. Adds prior if necessary
% ------------------------------------------------------------------------------
if analytic_derivation
if full_Hess,
[lnprior, dlnprior, d2lnprior] = priordens(xparam1,BayesInfo.pshape,BayesInfo.p6,BayesInfo.p7,BayesInfo.p3,BayesInfo.p4);
Hess = Hess - d2lnprior;
else
[lnprior, dlnprior] = priordens(xparam1,BayesInfo.pshape,BayesInfo.p6,BayesInfo.p7,BayesInfo.p3,BayesInfo.p4);
end
if no_DLIK==0
DLIK = DLIK - dlnprior';
end
if outer_product_gradient,
dlik = lik1{2};
dlik=[- dlnprior; dlik(start:end,:)];
Hess = dlik'*dlik;
end
else
lnprior = priordens(xparam1,BayesInfo.pshape,BayesInfo.p6,BayesInfo.p7,BayesInfo.p3,BayesInfo.p4);
end
fval = (likelihood-lnprior);
if isnan(fval)
info = 47;
exit_flag = 0;
return
end
if imag(fval)~=0
info = 48;
exit_flag = 0;
return
end
% Update DynareOptions.kalman_algo.
DynareOptions.kalman_algo = kalman_algo;
% Update the penalty.
penalty = fval;
if analytic_derivation==0 && nargout==2,
lik=lik(start:end,:);
DLIK=[-lnprior; lik(:)];
end