[R-SIG-Finance] MAR-GARCH

[Nigel.Walker at studentmail.newcastle.edu.au]

Hi list,
I am looking at ways to estimate a MAR-GARCH model. What i would like to do is maximise the likelihood function  to obtain the parameters however i am not sure how to do this. I was thinking of using optim but am not sure how to. The problem is i have ht, et, and tau that depend on the parameters i wish to obtain. These ht's, et's and tau's are within the liklihood function. 

The code below is an example of what i need to calculate in order to obtain the likelihood function. The likelihood function is also given. Does anyone know how i would go about maximising the likelihood to obtain the estimates? 
note that n is the length of the series and the parameters(phis, beta's and gamma's) are first set to initials. 
Any help would be very welcome

ht1<-c()
ht1[1]<-1
ht2<-c()
ht2[1]<-1
et1<-c()
et1[1]<-1
et1<-c()
et2[1]<-1
denominator1<-c()
denominator1[1]<-1
denominator2<-c()
denominator2[1]<-1
top1<-c()
top1[1]<-1
top2<-c()
top2[1]<-1
for (L in 2:n){
ht1[L]=beta10+beta11*(et1[L-1])^2+gamma11*ht1[L-1];
et1[L]<- rnorm(1,0,sqrt(ht1[L]));
#yt[L]=phi10+phi11*yt[L-1]+et1[L-1]
ht2[L]=beta20+beta21*(et2[L-1])^2+gamma21*ht2[L-1];
et2[L] <- rnorm(1,0,sqrt(ht2[L]))
#yt[L]=phi20+phi21*yt[L-1]+et2[L-1]
denominator1[L]<-alpha1*(1/sqrt(ht1[L]))*dnorm(et1[L]/sqrt(ht1[L]))
denominator2[L]<- alpha2*(1/sqrt(ht2[L]))*dnorm(et2[L]/sqrt(ht2[L]))
top1[L]<-alpha1*(1/sqrt(ht1[L]))*dnorm(et1[L]/sqrt(ht1[L]))
top2[L]<-alpha2*(1/sqrt(ht2[L]))*dnorm(et2[L]/sqrt(ht2[L]))
}

# Now to get up tau
denominator<-denominator1+denominator2
tau1<-top1/denominator
tau2<-top2/denominator
lik.p1<-tau1*log(alpha1)+tau2*log(alpha2)
lik.p2<- (tau1*log(ht1))/2+(tau2*log(ht2))/2
lik.p3<- (tau1*et1^2)/(2*ht1)+(tau2*et2^2)/(2*ht2)
likeli<- lik.p1-lik.p2-lik.p3
likelihood<- sum(likeli[3:n])