# Transformation of GARCH Equation to multiple-day Forecast Equation

I want to understand the procedure of how to predict with the GARCH Modell. Therefore it is said that a one day ahead forecast is easy due to the fact that the GARCH equation can produce this. Furthermore forecasts for more than one day can be achieved by recursive substitution according to Rachev (Financial Econometrics):

Somehow I don't get how the equation is transformed. I always stuck at the point where I would substitute the variance with 8.34 and expand the equation to a sum. However I would never come to the point where it looks like 8.35.

Thanks a lot! Clemens

• the formula 8.35 is wrong, I recommend that you find another book ! – Malick Aug 5 '16 at 22:01
• You could show what you are getting instead of 8.35, and we could see if we agree with you. If Malick says 8.35 is wrong, this makes even more sense. Also, I think this fits better at Cross Validated. I suggest it to be moved there. (If the moderators agree to migrate the question, that could be better than just cross posting there.) – Richard Hardy Aug 8 '16 at 19:46