98 lines
3.3 KiB
Matlab
98 lines
3.3 KiB
Matlab
function LIK = DiffuseLikelihoodH3corr(T,R,Q,H,Pinf,Pstar,Y,trend,start)
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% stephane.adjemian@cepremap.cnrs.fr [12-13-2004]
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%
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% Same as DiffuseLikelihoodH3 but allows correlation between the measurement
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% errors (this is not a problem with the multivariate approach).
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global bayestopt_ options_
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mf = bayestopt_.mf;
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pp = size(Y,1);
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mm = size(T,1);
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rr = size(Q,1);
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smpl = size(Y,2);
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T = cat(1,cat(2,T,zeros(mm,pp)),zeros(pp,mm+pp));
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R = cat(1,cat(2,R,zeros(mm,pp)),cat(2,zeros(pp,rr),eye(pp)));
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Q = cat(1,cat(2,Q,zeros(rr,pp)),cat(2,zeros(pp,rr),H));
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if size(Pinf,1) % Otherwise Pinf = 0 (no unit root)
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Pinf = cat(1,cat(2,Pinf,zeros(mm,pp)),zeros(pp,mm+pp));
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end
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Pstar = cat(1,cat(2,Pstar,zeros(mm,pp)),cat(2,zeros(pp,mm),H));
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a = zeros(mm+pp,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(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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newRank = rank(Pinf,crit);
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while rank(Pinf,crit) & t < smpl %% Matrix Finf is assumed to be zero
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t = t+1;
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for i=1:pp
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v(i) = Y(i,t)-a(mf(i))-a(mm+i)-trend(i,t);
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Fstar = Pstar(mf(i),mf(i))+Pstar(mm+i,mm+i);
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Finf = Pinf(mf(i),mf(i));
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Kstar = Pstar(:,mf(i))+Pstar(:,mm+i);
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if Finf > crit
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Kinf = Pinf(:,mf(i));
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a = a + Kinf*v(i)/Finf;
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Pstar = Pstar + Kinf*transpose(Kinf)*Fstar/(Finf*Finf) - ...
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(Kstar*transpose(Kinf)+Kinf*transpose(Kstar))/Finf;
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Pinf = Pinf - Kinf*transpose(Kinf)/Finf;
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lik(t) = lik(t) + log(Finf);
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else %% 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) == 0
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lik(t) = lik(t) + log(Fstar) + v(i)*v(i)/Fstar;
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end
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a = a + Kstar*v(i)/Fstar;
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Pstar = Pstar - Kstar*transpose(Kstar)/Fstar;
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end
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oldRank = rank(Pinf,crit);
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a = T*a;
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Pstar = T*Pstar*transpose(T)+QQ;
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Pinf = T*Pinf*transpose(T);
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newRank = rank(Pinf,crit);
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if oldRank ~= newRank
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disp('DiffuseLiklihoodH3 :: T does influence the rank of Pinf!')
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end
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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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for i=1:pp
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v(i) = Y(i,t) - a(mf(i)) - trend(i,t) -a(mm+i);
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Fi = Pstar(mf(i),mf(i))+Pstar(mm+i,mm+i);
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if Fi > crit
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Ki = Pstar(:,mf(i))+Pstar(:,mm+i);
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a = a + Ki*v(i)/Fi;
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Pstar = Pstar - Ki*transpose(Ki)/Fi;
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lik(t) = lik(t) + log(Fi) + v(i)*v(i)/Fi;
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end
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end
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oldP = Pstar;
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a = T*a;
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Pstar = T*Pstar*transpose(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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for i=1:pp
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v(i) = Y(i,t) - a(mf(i)) - trend(i,t) - a(mm+i);
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Fi = Pstar(mf(i),mf(i))+Pstar(mm+i,mm+i);
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if Fi > crit
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Ki = Pstar(:,mf(i))+Pstar(:,mm+i);
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a = a + Ki*v(i)/Fi;
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Pstar = Pstar - Ki*transpose(Ki)/Fi;
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lik(t) = lik(t) + log(Fi) + v(i)*v(i)/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); |