Good algorithm for maximum likelihood estimation

Question

I have a problem. I need to estimate some statistics with GARCH/ARCH model. In Matlab I use something like this:

 spec = garchset('P', 1, 'Q', 1)
 [fit01,~,LogL01] =garchfit(spec, STAT);

so this returns three parameters of GARCH model with maximum likelihood. But I really need to how which algorithm is used in garchfit , because I need to write a program which makes the same work in estimating parameters automatically.

My program works now very slow and sometimes not correct. So the questions are:

1. How get the code of garchfit or MLE in Matlab?
2. Does anyone know some good and fast algorithm on MLE?

(MLE = maximum likelihood estimation)

Answer 1

To see the code (if possible) you can type edit garchfit.

From the documentation of garchfit I have found some recommendations:

garchfit will be removed in a future release. Use estimate, estimate, estimate, or estimate instead.

My guess is that you want to look into garch.estimate.