mvar.m

 function [IP,pf,A,pb,B,ef,eb,vaic,Vaicv]=mvar(u,maxIP,alg,criterion)
% Estimate MVAR
%
%[IP,pf,A,pb,B,ef,eb,vaic,Vaicv] = mvar(u,maxIP,alg,criterion)
%
% input: u     - data rows
%        maxIP - externaly defined maximum IP
%        alg   - for algorithm (=1 Nutall-Strand), (=2 - mlsm) ,
%                              (=3 - Vieira Morf), (=4 - QR artfit)
%        criterion for order choice - 0: MDL
%                                     1: AIC; 2: Hanna-Quinn, 3 Schwartz,
%                                     4: FPE, 5 - fixed order in maxIP
% output: See Data Structure Data Base
%

[nSegLength,nChannels] = size(u');
if nargin<3, alg=1; criterion=1; end % defaults
if nargin<4, criterion=1; end        % defaults

if criterion==5 % Fixed order in maxIP
   if maxIP==0
      pf=u*u';     % Eq. (15.90) Equation numbering refers to Marple Jr.
      pb=pf;       % Eq. (15.90)
      ef=u;
      eb=u;
      npf=size(pf);
      A=zeros(npf,npf,0);
      B=A;
      vaic=det(pf);
      Vaicv=det(pf);
      IP=0;
      return
   end
   IP=maxIP;
   switch alg      %  Formula from Marple Jr.
      case 1,
         [pf A pb B ef eb]=mcarns(u,IP);
         pf=pf(:,:)/nSegLength; %Nuttall-Strand needs scaling.
      case 2,
         [pf A ef]=cmlsm(u,IP);
         B  = [ ]; eb = [ ]; pb = [ ];
         pf=pf(:,:)/nSegLength;
      case 3,
         [pf A pb B ef eb]=mcarvm(u,IP);
         pf=pf(:,:)/nSegLength; %Vieira-Morf needs scaling.
      case 4,
         [pf A ef]=arfitcaps(u,IP);
         B  = [ ]; eb = [ ]; pb = [ ];
         % Arfit does not need scaling. pf=pf;
   end

   vaic=length(u)*log(det(pf))+2*(nChannels*nChannels)*IP;

   Vaicv=vaic;
   fprintf('IP=%0.f  vaic=%f\n',IP,vaic);
   return
end
%
vaicv=0;
if nargin<2
   maxOrder=30;
   disp(['maxOrder limited to ' int2str(maxOrder)])
   UpperboundOrder = round(3*sqrt(nSegLength)/nChannels); % Marple Jr. p. 409
   % Suggested by Nuttall, 1976.
   UpperboundOrder = min([maxOrder UpperboundOrder]);
else
   maxOrder=maxIP;
   UpperboundOrder=maxIP;
   disp(['maxOrder limited to ' int2str(maxOrder)])
end
IP=1;
Vaicv=zeros(maxOrder+1,1);
while IP <= UpperboundOrder,
   switch alg
      case 1,
         %  Formula from Marple Jr.
         [npf na npb nb nef neb]=mcarns(u,IP);
      case 2,
         [npf na nef]=cmlsm(u,IP);
      case 3,
         [npf na npb nb nef neb]=mcarvm(u,IP);
      case 4,
         [npf na nef]=arfitcaps(u,IP);
   end
   %  criterion
   flgTesting=0;
   if flgTesting
      disp('Criteria testing routine')
      switch criterion
         case 1, % AIC
            vaic=length(u)*log(det(npf)) ...
                 +2*(nChannels+nChannels*nChannels*IP);
         case 2,  % Hannan-Quinn
            vaic=length(u)*log(det(npf)) ...
                 + 2*log(log(length(u)))*(nChannels+(nChannels*nChannels)*IP);
         case 3, % Schwartz
            vaic=length(u)*log(det(npf)) ...
                 +(log(length(u)))*(nChannels+(nChannels*nChannels)*IP);
         case 4, % FPE
            vaic=log(det(npf)*((length(u)+nChannels*IP+1) ...
                                  /length(u)-nChannels*IP-1)^nChannels);
         otherwise
            %nop
      end
   else
      switch criterion
         case 1, % AIC
            vaic=length(u)*log(det(npf)) ...
                 +2*(nChannels*nChannels)*IP;
         case 2,  % Hannan-Quinn
            vaic=length(u)*log(det(npf)) ...
                 + 2*log(log(length(u)))*(nChannels*nChannels)*IP;
         case 3, % Schwartz
            vaic=length(u)*log(det(npf)) ...
                 +(log(length(u)))*(nChannels*nChannels)*IP;
         case 4, % FPE
            vaic=log(det(npf)*((length(u)+nChannels*IP+1) ...
                                  /length(u)-nChannels*IP-1)^nChannels);
         otherwise
            %nop
      end
   end;
   Vaicv(IP+1)=vaic;
   fprintf('IP=%0.f  vaic=%f\n',IP,vaic);
   if (vaic>vaicv) && (IP~=1),
      vaic=vaicv;
      break;
   end; % Akaike condition
   vaicv=vaic;
   pf = npf;
   A  = na;
   ef = nef;
   if alg==1
      B  = nb;
      eb = neb;
      pb = npb;
   else % review status for backward prediction in clmsm
      B  = [ ];
      eb = [ ];
      pb = [ ];
   end
   IP=IP+1;
end;

disp(' ')
IP=IP-1;
vaic=vaicv;
Vaicv=Vaicv(2:IP+1);

switch alg
   case {1,3}, %Nuttall-Strand and Vieira-Morf need scaling.
      pf=pf(:,:)/nSegLength;
   case 4,
      pf=pf; % arfit does not need scaling.
   otherwise  %
      pf=pf(:,:)/nSegLength;
end;