/usr/share/dynare/matlab/AHessian.m is in dynare-common 4.4.1-1build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 | function [AHess, DLIK, LIK] = AHessian(T,R,Q,H,P,Y,DT,DYss,DOm,DH,DP,start,mf,kalman_tol,riccati_tol)
% function [AHess, DLIK, LIK] = AHessian(T,R,Q,H,P,Y,DT,DYss,DOm,DH,DP,start,mf,kalman_tol,riccati_tol)
%
% computes the asymptotic hessian matrix of the log-likelihood function of
% a state space model (notation as in kalman_filter.m in DYNARE
% Thanks to Nikolai Iskrev
%
% NOTE: the derivative matrices (DT,DR ...) are 3-dim. arrays with last
% dimension equal to the number of structural parameters
% 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/licen
k = size(DT,3); % number of structural parameters
smpl = size(Y,2); % Sample size.
pp = size(Y,1); % Maximum number of observed variables.
mm = size(T,2); % Number of state variables.
a = zeros(mm,1); % State vector.
Om = R*Q*transpose(R); % Variance of R times the vector of structural innovations.
t = 0; % Initialization of the time index.
oldK = 0;
notsteady = 1; % Steady state flag.
F_singular = 1;
lik = zeros(smpl,1); % Initialization of the vector gathering the densities.
LIK = Inf; % Default value of the log likelihood.
if nargout > 1,
DLIK = zeros(k,1); % Initialization of the score.
end
AHess = zeros(k,k); % Initialization of the Hessian
Da = zeros(mm,k); % State vector.
Dv = zeros(length(mf),k);
% for ii = 1:k
% DOm = DR(:,:,ii)*Q*transpose(R) + R*DQ(:,:,ii)*transpose(R) + R*Q*transpose(DR(:,:,ii));
% end
while notsteady && t<smpl
t = t+1;
v = Y(:,t)-a(mf);
F = P(mf,mf) + H;
if rcond(F) < kalman_tol
if ~all(abs(F(:))<kalman_tol)
return
else
a = T*a;
P = T*P*transpose(T)+Om;
end
else
F_singular = 0;
iF = inv(F);
K = P(:,mf)*iF;
lik(t) = log(det(F))+transpose(v)*iF*v;
[DK,DF,DP1] = computeDKalman(T,DT,DOm,P,DP,DH,mf,iF,K);
for ii = 1:k
Dv(:,ii) = -Da(mf,ii) - DYss(mf,ii);
Da(:,ii) = DT(:,:,ii)*(a+K*v) + T*(Da(:,ii)+DK(:,:,ii)*v + K*Dv(:,ii));
if t>=start && nargout > 1
DLIK(ii,1) = DLIK(ii,1) + trace( iF*DF(:,:,ii) ) + 2*Dv(:,ii)'*iF*v - v'*(iF*DF(:,:,ii)*iF)*v;
end
end
vecDPmf = reshape(DP(mf,mf,:),[],k);
% iPmf = inv(P(mf,mf));
if t>=start
AHess = AHess + Dv'*iF*Dv + .5*(vecDPmf' * kron(iF,iF) * vecDPmf);
end
a = T*(a+K*v);
P = T*(P-K*P(mf,:))*transpose(T)+Om;
DP = DP1;
end
notsteady = max(max(abs(K-oldK))) > riccati_tol;
oldK = K;
end
if F_singular
error('The variance of the forecast error remains singular until the end of the sample')
end
if t < smpl
t0 = t+1;
while t < smpl
t = t+1;
v = Y(:,t)-a(mf);
for ii = 1:k
Dv(:,ii) = -Da(mf,ii)-DYss(mf,ii);
Da(:,ii) = DT(:,:,ii)*(a+K*v) + T*(Da(:,ii)+DK(:,:,ii)*v + K*Dv(:,ii));
if t>=start && nargout >1
DLIK(ii,1) = DLIK(ii,1) + trace( iF*DF(:,:,ii) ) + 2*Dv(:,ii)'*iF*v - v'*(iF*DF(:,:,ii)*iF)*v;
end
end
if t>=start
AHess = AHess + Dv'*iF*Dv;
end
a = T*(a+K*v);
lik(t) = transpose(v)*iF*v;
end
AHess = AHess + .5*(smpl-t0+1)*(vecDPmf' * kron(iF,iF) * vecDPmf);
if nargout > 1
for ii = 1:k
% DLIK(ii,1) = DLIK(ii,1) + (smpl-t0+1)*trace( iF*DF(:,:,ii) );
end
end
lik(t0:smpl) = lik(t0:smpl) + log(det(F));
% for ii = 1:k;
% for jj = 1:ii
% H(ii,jj) = trace(iPmf*(.5*DP(mf,mf,ii)*iPmf*DP(mf,mf,jj) + Dv(:,ii)*Dv(:,jj)'));
% end
% end
end
AHess = -AHess;
if nargout > 1,
DLIK = DLIK/2;
end
% adding log-likelihhod constants
lik = (lik + pp*log(2*pi))/2;
LIK = sum(lik(start:end)); % Minus the log-likelihood.
% end of main function
function [DK,DF,DP1] = computeDKalman(T,DT,DOm,P,DP,DH,mf,iF,K)
k = size(DT,3);
tmp = P-K*P(mf,:);
for ii = 1:k
DF(:,:,ii) = DP(mf,mf,ii) + DH(:,:,ii);
DiF(:,:,ii) = -iF*DF(:,:,ii)*iF;
DK(:,:,ii) = DP(:,mf,ii)*iF + P(:,mf)*DiF(:,:,ii);
Dtmp = DP(:,:,ii) - DK(:,:,ii)*P(mf,:) - K*DP(mf,:,ii);
DP1(:,:,ii) = DT(:,:,ii)*tmp*T' + T*Dtmp*T' + T*tmp*DT(:,:,ii)' + DOm(:,:,ii);
end
% end of computeDKalman
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