Hi!I have a question concerning volatility forecasting.If I use GARCH(1,1), h(t)=a0+a1*u(t-1)^2+b1*h(t-1). In the estimation part of a0, a1 and b1, I have read that the global surface (a0,a1,b1) is vary flat but locally its not which make the optimizing part vary difficult. I have also heard that one can solve that problem by:(i) Use the unconditional variance, var, to solve the parameter a0, a0=var*(1-a1-b1), which leave me with just two variables to estimate. By doing a coordinate transformation, (a1,b1) to (z1,z2) wherez1=log(-log(my1)), z2=log(-log(my2)), my1=a1/(1-my2), my2=a1+b1This should simplify the optimizing situation because the global surface become no flat and no constrains will be needed.(ii) Use a filter where a global grid search is used. Around this point a local GN gradient search is done. I am not in full understanding of this one.I think the most of the math in (i) and (ii) can be found in - Zumbach, G.(2000) "The Pitfalls in Fitting GARCH(1,1) Processes"Hope someone have any ideas. Especially any good articles in the area of (i) and (ii) or if someone already have done this.Regards,Buster

One other thing.Matthew C Roberts, if you are reading this. In one post you are suggesting to take the return series*100 to get a better estimation. When I am using the scale the parameters a1 and b1 have the sum quite close to 1 (unstationary). Can you give a "good" explanation in this? I have no good insight?Thanks very much.Regards,Buster

In my routines, I don't use either process. I simply use brute force MLE. I have more than once performed analysis of the parameter fit, i.e. plotting the ML across different param values, but the real question is to ask whether you care--in most of my applications, some deviation b/c of a lack of global convergence doesn't really matter, as long as the local convergence isn't "too" far from the global minimum. That's fuzzy, I realize, but in my case, I've never had much of a problem, but I've been sent data that is much less well-behaved, and if I had to work on that data (i.e. if people would _pay_ me for my opinion ) I would resort to some of the other techniques. But I've never had much problem with simple MLE.As for a+b~1, its very common, if you read the literature on FIGARCH, you'll find that almost any process that exhibits GARCH tendencies is better described as a FIGARCH process. I don't typically worry too much about it, unless I am specifically seeking to show FIGARCH effects. For forecasting, the difference b/t GARCH & FIGARCH is small for short horizons--how many periods are you forecasting ahead?Matt.

Matt,Thanks for your answer.I will take a look on FIGARCH.Regarding the forecast horizon, I want to compare the implied vol term structure and the GARCH term structure for both foreign exchange rate and interest rate as underlying for options. For foreign exchange rate I am interested in 90 days maximum and for the interest rate 500 days maximum.How much money were you talking about? (To work on less well-behaved data) .Thanks again.Buster