DiffuseLikelihood1

 M. Ratto added lik in output
 stephane.adjemian@cepremap.cnrs.fr [07-19-2004]

 Same as DiffuseLikelihoodH1 without measurement error.

0001 function [LIK, lik] = DiffuseLikelihood1(T,R,Q,Pinf,Pstar,Y,trend,start)
0002 % M. Ratto added lik in output
0003 % stephane.adjemian@cepremap.cnrs.fr [07-19-2004]
0004 %
0005 % Same as DiffuseLikelihoodH1 without measurement error.
0006   global bayestopt_ options_
0007   
0008   mf = bayestopt_.mf;
0009   smpl = size(Y,2);
0010   mm   = size(T,2);
0011   pp   = size(Y,1);
0012   a    = zeros(mm,1);
0013   dF = 1;
0014   QQ   = R*Q*transpose(R);
0015   t    = 0;
0016   lik  = zeros(smpl+1,1);
0017   LIK  = Inf;
0018   lik(smpl+1) = smpl*pp*log(2*pi);
0019   notsteady   = 1;
0020   crit        = options_.kalman_tol;
0021   reste       = 0;
0022   while rank(Pinf,crit) & t < smpl
0023     t     = t+1;
0024     v        = Y(:,t)-a(mf)-trend(:,t);
0025     Finf  = Pinf(mf,mf);
0026     if rcond(Finf) < crit 
0027       if ~all(abs(Finf(:)) < crit)
0028     return
0029       else
0030     iFstar    = inv(Pstar(mf,mf));
0031     dFstar    = det(Pstar(mf,mf));
0032     Kstar    = Pstar(:,mf)*iFstar;
0033     lik(t)    = log(dFstar) + transpose(v)*iFstar*v;
0034     Pinf    = T*Pinf*transpose(T);
0035     Pstar    = T*(Pstar-Pstar(:,mf)*transpose(Kstar))*transpose(T)+QQ;
0036     a        = T*(a+Kstar*v);
0037       end
0038     else
0039       lik(t)    = log(det(Finf));
0040       iFinf    = inv(Finf);
0041       Kinf    = Pinf(:,mf)*iFinf;                    %%    premultiplication by the transition matrix T is removed (stephane)
0042       Fstar    = Pstar(mf,mf);
0043       Kstar    = (Pstar(:,mf)-Kinf*Fstar)*iFinf;     %%    premultiplication by the transition matrix T is removed (stephane)
0044       Pstar    = T*(Pstar-Pstar(:,mf)*transpose(Kinf)-Pinf(:,mf)*transpose(Kstar))*transpose(T)+QQ;
0045       Pinf    = T*(Pinf-Pinf(:,mf)*transpose(Kinf))*transpose(T);
0046       a        = T*(a+Kinf*v);                    
0047     end  
0048   end
0049   if t == smpl                                                           
0050     error(['There isn''t enough information to estimate the initial' ... 
0051        ' conditions of the nonstationary variables']);                   
0052   end                                                                    
0053   F_singular = 1;
0054   while notsteady & t < smpl
0055     t  = t+1;
0056     v        = Y(:,t)-a(mf)-trend(:,t);
0057     F  = Pstar(mf,mf);
0058     oldPstar  = Pstar;
0059     dF = det(F);
0060     if rcond(F) < crit 
0061       if ~all(abs(F(:))<crit)
0062     return
0063       else
0064     a         = T*a;
0065     Pstar     = T*Pstar*transpose(T)+QQ;
0066       end
0067     else
0068       F_singular = 0;
0069       iF        = inv(F);
0070       lik(t)    = log(dF)+transpose(v)*iF*v;
0071       K         = Pstar(:,mf)*iF; %% premultiplication by the transition matrix T is removed (stephane)
0072       a         = T*(a+K*v);        %% --> factorization of the transition matrix...
0073       Pstar     = T*(Pstar-K*Pstar(mf,:))*transpose(T)+QQ;    %% ... idem (stephane)
0074     end
0075     notsteady = ~(max(max(abs(Pstar-oldPstar)))<crit);
0076   end
0077   if F_singular == 1
0078     error(['The variance of the forecast error remains singular until the' ...
0079       'end of the sample'])
0080   end
0081   reste = smpl-t;
0082   while t < smpl
0083     t = t+1;
0084     v = Y(:,t)-a(mf)-trend(:,t);
0085     a = T*(a+K*v);
0086     lik(t) = transpose(v)*iF*v;
0087   end
0088   lik(t) = lik(t) + reste*log(dF);
0089 
0090 
0091   LIK    = .5*(sum(lik(start:end))-(start-1)*lik(smpl+1)/smpl);% Minus the log-likelihood.