GARCH estimation

*To*: mathgroup at yoda.physics.unc.edu*Subject*: GARCH estimation*From*: karjalaine22 at joshua.wharton.upenn.edu (Risto Karjalainen)*Date*: Tue, 13 Apr 93 11:19:27 EDT

I'm trying to estimate a GARCH model for a long time series (5000+ data points), and was wondering if somebody has already implemented a maximum likelihood estimator in Mathematica. The model is, e.g., x = b0 + b1 x + b2 x + e t t-1 t-2 t e ~ N(0,h ) t t 2 h = alpha0 + alpha1 e + beta1 h t t-1 t-1 I wrote a straihtforward MLE for the model, following the original papers of Engle and Bollerslev in mid 80's on the topic. However, using FindMinimum does not seem to allow for constraints easily (estimates of alpha and beta should be >= 0); also, estimation is very time-consuming. So, I would appreciate any suggestions on: 1. Are there any packages available that would do this kind of thing ? (I couldn't find anything in mathsource) 2. Are there any packages that do constrained numerical optimization (which I could then adapt to the maximization of log likelihood) ? 3. Any other ways to do the estimation (none of the other packages I looked at (Splus, SAS, TSP, RATS.,..) seem to do what I need) ? Thanks a lot, --Risto Karjalainen