varprior

function [ydum,xdum,breaks]=varprior(nv,nx,lags,mnprior,vprior)
 ydum, xdum:   dummy observation data that implement the prior
 breaks:       vector of points in the dummy data after which new dummy obs's start
                   Set breaks=T+[0;breaks], ydata=[ydata;ydum], xdum=[xdata;xdum], where 
                   actual data matrix has T rows, in preparing input for rfvar3
 nv,nx,lags: VAR dimensions
 mnprior.tight:Overall tightness of Minnesota prior
 mnprior.decay:Standard deviations of lags shrink as lag^(-decay)
 vprior.sig:   Vector of prior modes for diagonal elements of r.f. covariance matrix
 vprior.w:     Weight on prior on vcv.  1 corresponds to "one dummy observation" weight
                   Should be an integer, and will be rounded if not.  vprior.sig is needed
                   to scale the Minnesota prior, even if the prior on sigma is not used itself.
                   Set vprior.w=0 to achieve this.
 Note:         The original Minnesota prior treats own lags asymmetrically, and therefore
                   cannot be implemented entirely with dummy observations.  It is also usually
                   taken to include the sum-of-coefficients and co-persistence components
                   that are implemented directly in rfvar3.m.  The diagonal prior on v, combined
                   with sum-of-coefficients and co-persistence components and with the unit own-first-lag
                   prior mean generates larger prior variances for own than for cross-effects even in 
                   this formulation, but here there is no way to shrink toward a set of unconstrained 
                   univariate AR's.
-----------------------

0001 function [ydum,xdum,breaks]=varprior(nv,nx,lags,mnprior,vprior)
0002 %function [ydum,xdum,breaks]=varprior(nv,nx,lags,mnprior,vprior)
0003 % ydum, xdum:   dummy observation data that implement the prior
0004 % breaks:       vector of points in the dummy data after which new dummy obs's start
0005 %                   Set breaks=T+[0;breaks], ydata=[ydata;ydum], xdum=[xdata;xdum], where
0006 %                   actual data matrix has T rows, in preparing input for rfvar3
0007 % nv,nx,lags: VAR dimensions
0008 % mnprior.tight:Overall tightness of Minnesota prior
0009 % mnprior.decay:Standard deviations of lags shrink as lag^(-decay)
0010 % vprior.sig:   Vector of prior modes for diagonal elements of r.f. covariance matrix
0011 % vprior.w:     Weight on prior on vcv.  1 corresponds to "one dummy observation" weight
0012 %                   Should be an integer, and will be rounded if not.  vprior.sig is needed
0013 %                   to scale the Minnesota prior, even if the prior on sigma is not used itself.
0014 %                   Set vprior.w=0 to achieve this.
0015 % Note:         The original Minnesota prior treats own lags asymmetrically, and therefore
0016 %                   cannot be implemented entirely with dummy observations.  It is also usually
0017 %                   taken to include the sum-of-coefficients and co-persistence components
0018 %                   that are implemented directly in rfvar3.m.  The diagonal prior on v, combined
0019 %                   with sum-of-coefficients and co-persistence components and with the unit own-first-lag
0020 %                   prior mean generates larger prior variances for own than for cross-effects even in
0021 %                   this formulation, but here there is no way to shrink toward a set of unconstrained
0022 %                   univariate AR's.
0023 %-----------------------
0024 %
0025 if ~isempty(mnprior)
0026     xdum=zeros(lags+1,nx,lags,nv);
0027     ydum=zeros(lags+1,nv,lags,nv);
0028     for il=1:lags
0029         ydum(il+1,:,il,:)=il^mnprior.decay*diag(vprior.sig);
0030     end
0031     ydum(1,:,1,:)=diag(vprior.sig);
0032     ydum=mnprior.tight*reshape(ydum,[lags+1,nv,lags*nv]);
0033     ydum=flipdim(ydum,1);
0034     xdum=mnprior.tight*reshape(xdum,[lags+1,nx,lags*nv]);
0035     xdum=flipdim(xdum,1);
0036     breaks=(lags+1)*[1:(nv*lags)]';
0037     lbreak=breaks(end);
0038 else
0039     ydum=[];
0040     xdum=[];
0041     breaks=[];
0042     lbreak=0;
0043 end
0044 if ~isempty(vprior) & vprior.w>0
0045     ydum2=zeros(lags+1,nv,nv);
0046     xdum2=zeros(lags+1,nx,nv);
0047     ydum2(end,:,:)=diag(vprior.sig);
0048     ydum=cat(3,ydum,ydum2);
0049     xdum=cat(3,xdum,xdum2);
0050     dimy=size(ydum);
0051     ydum=reshape(permute(ydum,[1 3 2]),dimy(1)*dimy(3),nv);
0052     xdum=reshape(permute(xdum,[1 3 2]),dimy(1)*dimy(3),nx);
0053     breaks=[breaks;(lags+1)*[1:nv-1]'+lbreak];
0054 end