124 lines
4.1 KiB
Matlab
124 lines
4.1 KiB
Matlab
function [DLIK] = score(T,R,Q,H,P,Y,DT,DYss,DOm,DH,DP,start,mf,kalman_tol,riccati_tol)
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% function [DLIK] = score(T,R,Q,H,P,Y,DT,DYss,DOm,DH,DP,start,mf,kalman_tol,riccati_tol)
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%
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% computes the derivative of the log-likelihood function of
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% a state space model (notation as in kalman_filter.m in DYNARE
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% thanks to Nikolai Iskrev
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%
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% NOTE: the derivative matrices (DT,DR ...) are 3-dim. arrays with last
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% dimension equal to the number of structural parameters
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% Copyright (C) 2009-2017 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licen
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k = size(DT,3); % number of structural parameters
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smpl = size(Y,2); % Sample size.
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mm = size(T,2); % Number of state variables.
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a = zeros(mm,1); % State vector.
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Om = R*Q*transpose(R); % Variance of R times the vector of structural innovations.
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t = 0; % Initialization of the time index.
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oldK = 0;
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notsteady = 1; % Steady state flag.
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F_singular = 1;
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DLIK = zeros(k,1); % Initialization of the score.
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Da = zeros(mm,k); % State vector.
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Dv = zeros(length(mf),k); % observation vector.
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% for ii = 1:k
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% DOm = DR(:,:,ii)*Q*transpose(R) + R*DQ(:,:,ii)*transpose(R) + R*Q*transpose(DR(:,:,ii));
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% end
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while notsteady & t<smpl
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t = t+1;
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v = Y(:,t)-a(mf);
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F = P(mf,mf) + H;
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if rcond(F) < kalman_tol
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if ~all(abs(F(:))<kalman_tol)
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return
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else
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a = T*a;
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P = T*P*transpose(T)+Om;
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end
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else
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F_singular = 0;
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iF = inv(F);
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K = P(:,mf)*iF;
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[DK,DF,DP1] = computeDKalman(T,DT,DOm,P,DP,DH,mf,iF,K);
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for ii = 1:k
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Dv(:,ii) = -Da(mf,ii)-DYss(mf,ii);
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Da(:,ii) = DT(:,:,ii)*(a+K*v) + T*(Da(:,ii)+DK(:,:,ii)*v + K*Dv(:,ii));
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if t>=start
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DLIK(ii,1) = DLIK(ii,1) + trace( iF*DF(:,:,ii) ) + 2*Dv(:,ii)'*iF*v - v'*(iF*DF(:,:,ii)*iF)*v;
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end
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end
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a = T*(a+K*v);
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P = T*(P-K*P(mf,:))*transpose(T)+Om;
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DP = DP1;
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end
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notsteady = max(max(abs(K-oldK))) > riccati_tol;
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oldK = K;
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end
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if F_singular
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error('The variance of the forecast error remains singular until the end of the sample')
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end
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for ii = 1:k
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tmp0(:,:,ii) = iF*DF(:,:,ii)*iF;
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end
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if t < smpl
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t0 = t+1;
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while t < smpl
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t = t+1;
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v = Y(:,t)-a(mf);
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for ii = 1:k
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Dv(:,ii) = -Da(mf,ii)-DYss(mf,ii);
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Da(:,ii) = DT(:,:,ii)*(a+K*v) + T*(Da(:,ii)+DK(:,:,ii)*v + K*Dv(:,ii));
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if t>=start
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DLIK(ii,1) = DLIK(ii,1) + trace( iF*DF(:,:,ii) ) + 2*Dv(:,ii)'*iF*v - v'*(iF*DF(:,:,ii)*iF)*v;
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end
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end
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a = T*(a+K*v);
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end
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for ii = 1:k
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% DLIK(ii,1) = DLIK(ii,1) + (smpl-t0+1)*trace( iF*DF(:,:,ii) );
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end
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end
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DLIK = DLIK/2;
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% end of main function
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function [DK,DF,DP1] = computeDKalman(T,DT,DOm,P,DP,DH,mf,iF,K)
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k = size(DT,3);
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tmp = P-K*P(mf,:);
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for ii = 1:k
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DF(:,:,ii) = DP(mf,mf,ii) + DH(:,:,ii);
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DiF(:,:,ii) = -iF*DF(:,:,ii)*iF;
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DK(:,:,ii) = DP(:,mf,ii)*iF + P(:,mf)*DiF(:,:,ii);
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Dtmp = DP(:,:,ii) - DK(:,:,ii)*P(mf,:) - K*DP(mf,:,ii);
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DP1(:,:,ii) = DT(:,:,ii)*tmp*T' + T*Dtmp*T' + T*tmp*DT(:,:,ii)' + DOm(:,:,ii);
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end
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% end of computeDKalman
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