92 lines
3.0 KiB
Matlab
92 lines
3.0 KiB
Matlab
function [LIK, lik] = DiffuseLikelihood1(T,R,Q,Pinf,Pstar,Y,trend,start)
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% M. Ratto added lik in output
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% stephane.adjemian@cepremap.cnrs.fr [07-19-2004]
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%
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% Same as DiffuseLikelihoodH1 without measurement error.
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global bayestopt_ options_
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mf = bayestopt_.mf;
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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)-a(mf)-trend(:,t);
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Finf = Pinf(mf,mf);
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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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iFstar = inv(Pstar(mf,mf));
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dFstar = det(Pstar(mf,mf));
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Kstar = Pstar(:,mf)*iFstar;
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lik(t) = log(dFstar) + transpose(v)*iFstar*v;
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Pinf = T*Pinf*transpose(T);
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Pstar = T*(Pstar-Pstar(:,mf)*transpose(Kstar))*transpose(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(:,mf)*iFinf; %% premultiplication by the transition matrix T is removed (stephane)
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Fstar = Pstar(mf,mf);
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Kstar = (Pstar(:,mf)-Kinf*Fstar)*iFinf; %% premultiplication by the transition matrix T is removed (stephane)
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Pstar = T*(Pstar-Pstar(:,mf)*transpose(Kinf)-Pinf(:,mf)*transpose(Kstar))*transpose(T)+QQ;
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Pinf = T*(Pinf-Pinf(:,mf)*transpose(Kinf))*transpose(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)-a(mf)-trend(:,t);
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F = Pstar(mf,mf);
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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*transpose(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)+transpose(v)*iF*v;
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K = Pstar(:,mf)*iF; %% premultiplication by the transition matrix T is removed (stephane)
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a = T*(a+K*v); %% --> factorization of the transition matrix...
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Pstar = T*(Pstar-K*Pstar(mf,:))*transpose(T)+QQ; %% ... idem (stephane)
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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)-a(mf)-trend(:,t);
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a = T*(a+K*v);
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lik(t) = transpose(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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