Hey folks,Let's say I with information available today, I want to predict the volatility k days ahead, i.e. the expected volatility.In more detail, assume the following GARCH(1,1) model in equation (2):How would you derive the k-step-ahead expectations in equation (3)? I tried but cannot come up with it, even by inserting repeatedly.Your help is very much appreciated.Best regards,Steve

I never looked into forecasting using GARCH, but I remember reading a paper that mentions that multi-step volatility forecasting is hard due to non-linear nature of GARCH, and that it's easier to do a multi-step forecast if you use something called AGARCH(p,q) model instead. AGARCH is like GARCH, but in standard deviations instead of variances. Try to google AGARCH and GARCH in google scholar.You can also do a multi-step forecast by a Monte Carlo simulation. Linear forecast is just the time t expectation of what happens in time t+n. If you know that the model is, you can always simulate it to estimate this conditional expectation.

QuoteOriginally posted by: Steve06Hey folks,Let's say I with information available today, I want to predict the volatility k days ahead, i.e. the expected volatility.In more detail, assume the following GARCH(1,1) model in equation (2):How would you derive the k-step-ahead expectations in equation (3)? I tried but cannot come up with it, even by inserting repeatedly.Your help is very much appreciated.Best regards,SteveIt looks ok to me when k=1. If you agree, post your problem with k=2.