v4: added Kalman filter functions with explicit Z
git-svn-id: https://www.dynare.org/svn/dynare/dynare_v4@1621 ac1d8469-bf42-47a9-8791-bf33cf982152time-shift
michel
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function [LIK, lik] = DiffuseLikelihood1_Z(T,Z,R,Q,Pinf,Pstar,Y,trend,start)
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% function [LIK, lik] = DiffuseLikelihood1_Z(T,Z,R,Q,Pinf,Pstar,Y,trend,start)
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% Computes the diffuse likelihood without measurement error, in the case of a non-singular var-cov matrix
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%
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% INPUTS
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% T: mm*mm matrix
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% Z: pp,mm matrix
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% R: mm*rr matrix
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% Q: rr*rr matrix
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% Pinf: mm*mm diagonal matrix with with q ones and m-q zeros
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% Pstar: mm*mm variance-covariance matrix with stationary variables
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% Y: pp*1 vector
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% trend
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% start: likelihood evaluation at 'start'
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%
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% OUTPUTS
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% LIK: likelihood
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% lik: density vector in each period
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%
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% SPECIAL REQUIREMENTS
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% See "Filtering and Smoothing of State Vector for Diffuse State Space
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% Models", S.J. Koopman and J. Durbin (2003, in Journal of Time Series
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% Analysis, vol. 24(1), pp. 85-98).
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%
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% part of DYNARE, copyright Dynare Team (2004-2008)
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% Gnu Public License.
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% M. Ratto added lik in output
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global bayestopt_ options_
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smpl = size(Y,2);
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mm = size(T,2);
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pp = size(Y,1);
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a = zeros(mm,1);
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dF = 1;
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QQ = R*Q*transpose(R);
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t = 0;
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lik = zeros(smpl+1,1);
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LIK = Inf;
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lik(smpl+1) = smpl*pp*log(2*pi);
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notsteady = 1;
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crit = options_.kalman_tol;
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reste = 0;
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while rank(Pinf,crit) & t < smpl
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t = t+1;
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v = Y(:,t)-Z*a-trend(:,t);
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Finf = Z*Pinf*Z';
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if rcond(Finf) < crit
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if ~all(abs(Finf(:)) < crit)
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return
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else
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Fstar = Z*Pstar*Z';
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iFstar = inv(F);
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dFstar = det(F);
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Kstar = Pstar*Z'*iFstar;
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lik(t) = log(dFstar) + v'*iFstar*v;
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Pinf = T*Pinf*transpose(T);
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Pstar = T*(Pstar-Pstar*Z'*Kstar')*T'+QQ;
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a = T*(a+Kstar*v);
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end
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else
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lik(t) = log(det(Finf));
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iFinf = inv(Finf);
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Kinf = Pinf*Z'*iFinf;
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Fstar = Z*Pstar*Z';
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Kstar = (Pstar*Z'-Kinf*Fstar)*iFinf;
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Pstar = T*(Pstar-Pstar*Z'*Kinf'-Pinf*Z'*Kstar)*T'+QQ;
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Pinf = T*(Pinf-Pinf*Z'*Kinf')*T';
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a = T*(a+Kinf*v);
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end
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end
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if t == smpl
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error(['There isn''t enough information to estimate the initial' ...
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' conditions of the nonstationary variables']);
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end
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F_singular = 1;
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while notsteady & t < smpl
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t = t+1;
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v = Y(:,t)-Z*a-trend(:,t);
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F = Z*Pstar*Z';
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oldPstar = Pstar;
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dF = det(F);
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if rcond(F) < crit
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if ~all(abs(F(:))<crit)
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return
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else
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a = T*a;
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Pstar = T*Pstar*T'+QQ;
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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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lik(t) = log(dF)+v'*iF*v;
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K = Pstar*Z'*iF;
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a = T*(a+K*v);
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Pstar = T*(Pstar-K*Pstar*Z')*T'+QQ;
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end
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notsteady = ~(max(max(abs(Pstar-oldPstar)))<crit);
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end
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if F_singular == 1
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error(['The variance of the forecast error remains singular until the' ...
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'end of the sample'])
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end
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reste = smpl-t;
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while t < smpl
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t = t+1;
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v = Y(:,t)-Z*a-trend(:,t);
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a = T*(a+K*v);
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lik(t) = v*iF*v;
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end
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lik(t) = lik(t) + reste*log(dF);
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LIK = .5*(sum(lik(start:end))-(start-1)*lik(smpl+1)/smpl);% Minus the log-likelihood.
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@ -0,0 +1,169 @@
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function [LIK, lik] = DiffuseLikelihood3_Z(T,Z,R,Q,Pinf,Pstar,Y,trend,start)%//Z,T,R,Q,Pinf,Pstar,Y)
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% function [LIK, lik] = DiffuseLikelihood3(T,R,Q,Pinf,Pstar,Y,trend,start)
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% Computes the diffuse likelihood without measurement error, in the case of
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% a singular var-cov matrix.
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% Univariate treatment of multivariate time series.
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%
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% INPUTS
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% T: mm*mm matrix
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% Z: pp*mm matrix
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% R: mm*rr matrix
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% Q: rr*rr matrix
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% Pinf: mm*mm diagonal matrix with with q ones and m-q zeros
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% Pstar: mm*mm variance-covariance matrix with stationary variables
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% Y: pp*1 vector
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% trend
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% start: likelihood evaluation at 'start'
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%
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% OUTPUTS
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% LIK: likelihood
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% lik: density vector in each period
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%
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% SPECIAL REQUIREMENTS
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% See "Filtering and Smoothing of State Vector for Diffuse State Space
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% Models", S.J. Koopman and J. Durbin (2003, in Journal of Time Series
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% Analysis, vol. 24(1), pp. 85-98).
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%
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% part of DYNARE, copyright Dynare Team (2004-2008)
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% Gnu Public License.
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% M. Ratto added lik in output [October 2005]
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% changes by M. Ratto [April 2005]
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% introduced new options options_.diffuse_d for termination of DKF
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% new icc counter for Finf steps in DKF
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% new termination for DKF
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% likelihood terms for Fstar must be cumulated in DKF also when Pinf is non
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% zero.
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% [4/5/2005] correctyed bug in the modified verson of Ratto for rank of Pinf
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% introduced a specific crit1 for the DKF termination
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global bayestopt_ options_
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pp = size(Y,1);
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mm = size(T,1);
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smpl = size(Y,2);
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a = zeros(mm,1);
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QQ = R*Q*R';
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t = 0;
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lik = zeros(smpl+1,1);
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lik(smpl+1) = smpl*pp*log(2*pi); %% the constant of minus two times the log-likelihood
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notsteady = 1;
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crit = options_.kalman_tol;
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crit1 = 1.e-6;
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newRank = rank(Pinf,crit1);
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icc=0;
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while newRank & t < smpl
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t = t+1;
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for i=1:pp
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Zi = Z(i,:);
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v(i) = Y(i,t)-Zi*a-trend(i,t);
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Fstar = Zi*Pstar*Zi';
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Finf = Zi*Pinf*Zi';
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Kstar = Pstar*Zi';
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if Finf > crit & newRank
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icc=icc+1;
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Kinf = Pinf*Zi';
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a = a + Kinf*v(i)/Finf;
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Pstar = Pstar + Kinf*Kinf'*Fstar/(Finf*Finf) - ...
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(Kstar*Kinf'+Kinf*Kstar')/Finf;
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Pinf = Pinf - Kinf*Kinf'/Finf;
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lik(t) = lik(t) + log(Finf);
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if ~isempty(options_.diffuse_d),
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newRank = (icc<options_.diffuse_d);
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if newRank & (any(diag(Z*Pinf*Z')>crit)==0 & rank(Pinf,crit1)==0);
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options_.diffuse_d = icc;
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newRank=0;
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disp('WARNING: Change in OPTIONS_.DIFFUSE_D in univariate DKF')
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disp(['new OPTIONS_.DIFFUSE_D = ',int2str(icc)])
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disp('You may have to reset the optimisation')
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end
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else
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newRank = (any(diag(Z*Pinf*Z')>crit) | rank(Pinf,crit1));
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if newRank==0,
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P0= T*Pinf*T';
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newRank = (any(diag(Z*P0*Z')>crit) | rank(P0,crit1)); % M. Ratto 11/10/2005
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if newRank==0,
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options_.diffuse_d = icc;
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end
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end
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end,
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elseif Fstar > crit
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%% Note that : (1) rank(Pinf)=0 implies that Finf = 0, (2) outside this loop (when for some i and t the condition
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%% rank(Pinf)=0 is satisfied we have P = Pstar and F = Fstar and (3) Finf = 0 does not imply that
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%% rank(Pinf)=0. [stéphane,11-03-2004].
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%if rank(Pinf,crit) == 0
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% the likelihood terms should alwasy be cumulated, not only
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% when Pinf=0, otherwise the lik would depend on the ordering
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% of observed variables
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% presample options can be used to ignore initial time points
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lik(t) = lik(t) + log(Fstar) + v(i)*v(i)/Fstar;
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a = a + Kstar*v(i)/Fstar;
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Pstar = Pstar - Kstar*Kstar'/Fstar;
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else
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%disp(['zero F term in DKF for observed ',int2str(i),' ',num2str(Fstar)])
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end
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end
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if newRank,
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oldRank = rank(Pinf,crit1);
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else
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oldRank = 0;
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end
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a = T*a;
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Pstar = T*Pstar*T'+QQ;
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Pinf = T*Pinf*T';
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if newRank,
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newRank = rank(Pinf,crit1);
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end
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if oldRank ~= newRank
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disp('DiffuseLiklihood3 :: T does influence the rank of Pinf!')
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end
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end
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if t == smpl
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error(['There isn''t enough information to estimate the initial' ...
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' conditions of the nonstationary variables']);
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end
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while notsteady & t < smpl
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t = t+1;
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oldP = Pstar;
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for i=1:pp
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Zi = Z(i,:);
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v(i) = Y(i,t) - Zi*a - trend(i,t);
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Fi = Zi*Pstar*Zi';
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if Fi > crit
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Ki = Pstar*Zi';
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a = a + Ki*v(i)/Fi;
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Pstar = Pstar - Ki*Ki'/Fi;
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lik(t) = lik(t) + log(Fi) + v(i)*v(i)/Fi;
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else
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%disp(['zero F term for observed ',int2str(i),' ',num2str(Fi)])
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end
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end
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a = T*a;
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Pstar = T*Pstar*T' + QQ;
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notsteady = ~(max(max(abs(Pstar-oldP)))<crit);
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end
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while t < smpl
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t = t+1;
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Pstar = oldP;
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for i=1:pp
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Zi = Z(i,i);
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v(i) = Y(i,t) - Zi*a - trend(i,t);
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Fi = Zi*Pstar*Zi';
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if Fi > crit
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Ki = Pstar*Zi';
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a = a + Ki*v(i)/Fi;
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Pstar = Pstar - Ki*Ki'/Fi;
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lik(t) = lik(t) + log(Fi) + v(i)*v(i)/Fi;
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else
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%disp(['zero F term for observed ',int2str(i),' ',num2str(Fi)])
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end
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end
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a = T*a;
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end
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LIK = .5*(sum(lik(start:end))-(start-1)*lik(smpl+1)/smpl);
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