R help - Dec 2010 - Using nlminb for maximum likelihood estimation

I'm trying to estimate the parameters for GARCH(1,1) process.
Here's my code:
 
loglikelihood <-function(theta) {

h=((r[1]-theta[1])^2)
p=0

for (t in 2:length(r)) {
h=c(h,theta[2]+theta[3]*((r[t-1]-theta[1])^2)+theta[4]*h[t-1])
p=c(p,dnorm(r[t],theta[1],sqrt(h[t]),log=TRUE))
}

-sum(p)

}

 
Then I use nlminb to minimize the function loglikelihood:
 
nlminb( c(0.001,0.001,0.001,0.001), loglikelihood, lower=c(0.000001,0,0,0))
 
This does not produce a good result: the iteration limit is reached and
increasing it won't help. I have used "garchFit" from
fGarch-package to estimate the parameters. I set garchFit to use nlminb as well,
and it produces a result within just a few seconds.
However, for modification purposes, I need to get my own code working.
 
  		 	   		  
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Joonas - as_trix85 <ast_rix85 <at> hotmail.com> writes:
> 
> 
> I'm trying to estimate the parameters for GARCH(1,1) process.
> Here's my code:
> 
> loglikelihood <-function(theta) {
> 
> h=((r[1]-theta[1])^2)
> p=0
> 
> for (t in 2:length(r)) {
> h=c(h,theta[2]+theta[3]*((r[t-1]-theta[1])^2)+theta[4]*h[t-1])
> }
 It will be more efficient to set aside space for the full
h and p vectors (h <- p <- numeric(length(r))) rather than
building them up one step at a time.  Also, I think you can
compute p outside the loop:

 -sum(dnorm(r,theta[1],sqrt(h),log=TRUE))
> }
> 
>  
> Then I use nlminb to minimize the function loglikelihood:
> 
> nlminb( c(0.001,0.001,0.001,0.001), loglikelihood, lower=c(0.000001,0,0,0))
> 
> This does not produce a good result: the iteration limit 
> is reached and increasing it won't help. I have used
> "garchFit" from fGarch-package to estimate the parameters. 
> I set garchFit to use nlminb as well, and it
> produces a result within just a few seconds. 
> However, for modification purposes, I need to get my own code working.
  I don't see a question here, nor a reproducible example ...
can you look to see in more detail what garchFit does?  Does it
have a way to generate better starting parameter estimates?
Have you tried turning on tracing to see where your
approach is getting stuck?