I have been comparing the output of an R package to S+Finmetrics and I
notice that
the covariance matrix outputted by the two procedures is different. The
R package
computes the covariance matrix using Method 1 and I think ( but I'm not
sure ) that S+Finmetrics computes it
using Method 2.
I put in a correctionfactor (see below ) in to Method 2 in order to deal
with the fact that the var function
calculates the unnbiased estimate of variance. This gives the same
answer in both problems for the
data shown which I just made up. But, my hope is that , for much larger
problems, leaving the correction factor
out can maybe cause huge differences in the determinant ? That would
explain why some of the output ( AIC, BIC )
differs in the two packages. I'm not really sure how to check this
easily but if someone has an idea,
it would be appreciated. Basically, I kind of want to run some sort of
simulation along
the lines of below to check whether this could be the reason for the
differences. Thanks.
x<-c(11,12,13,14,16)
y<-c(2,4,6,8,12)
z<-c(14,18,22,50,20)
LHS<-cbind(x,y)
sample<-nrow(lhs)
# METHOD1
output1<-lm(LHS ~ z)
resids<-resid(output1)
sigma.hat1<-crossprod(resids)/sample
print(sigma.hat1)
print(det(sigma.hat1))
# METHOD2
fit1<-lm(LHS[,1] ~ z)
fit2<-lm(LHS[,2] ~ z)
correctionfactor<-sample-1/sample
sigma.hat2<-correctionfactor*var(cbind(resid(fit1),resid(fit2)))
print(sigma.hat2)
print(det(sigma.hat2))
