R/Par.star.R

In StVAR: Student's t Vector Autoregression (StVAR)

Par.star <-
function(a,S,MU,l,lag,v,T,M,c,TREND)
{

S <- BlockTop(a[((l*(l+1)/2)*(1-1)+1):((lag+3)*(l+1)*l/2)],l,lag)$S
if(c!=0) {MU <- matrix(c(a[(((lag+3)*(l+1)*l/2)+1):(((lag+3)*(l+1)*l/2)+l*c)]),l,c)}

if(c!=0) {M0 <- kronecker(diag(1,lag+1),MU)}
if(c==0) {M0 <- kronecker(diag(1,lag+1),0)}

if(c!=0) {M <- M0%*%t(TREND)} ; if (c==0) {M <- 0}

S11 <- S[1:l,1:l] ; S12 <- S[1:l,(l+1):(l*(lag+1))] ; S22 <- S[(l+1):(l*(lag+1)),(l+1):(l*(lag+1))]
SS <- solve(S22)  ; Q <- SS/v ; B1 <- SS%*%(S12) ; s2 <- S11-S12%*%SS%*%(S12) 


if(c!=0) {Delta0 <- MU[1:1,] - t(B1)%*%MU[c(rep(1:l,lag)),]}
if(c==0) {Delta0 <- 0}
beta <- cbind(Delta0, t(B1))

#Delta <- matrix(nrow=(T-lag),ncol=l)
#for(i in 1:(T-lag))
#{
#Delta[i,] <- M[1:1,i] - t(B1)%*%M[(1+1):nrow(M),i]
#}
 
#Delta0 <- MU - t(B1)%*%(kronecker(diag(ones(lag)),MU)) 

c.var <- s2[1,1]*vech(SS)/(v+l*lag-2)
var.coef <- c(v*s2[1,1]/(v+l*lag-2),c.var)

return(list(Delta0=Delta0,Q=Q,s2=s2,S=S,B1=B1,var.coef=var.coef))

}