I am a bit confused concerning some of the "underlying concepts" of ARMA & GARCH models. I know that ARMA models are meant to forecast the conditional mean of a process, while GARCH models are meant to forecast the conditional variance of that process. So far so good.
1) The first thing I am not sure about is wether the "autoregressive part" of an ARMA process is based on past estimations or past "true" ("observed") values ? Depending on the websites I found both answers and this really bothers me as they are different to me.
2) My second question is wether an ARMA model needs to be created at first place in order to get the error terms through an iterative process so we can "plug" these error terms into the GARCH model ? Or is it directly possible to model a GARCH process from a dataset ? Put differently are the error terms of an ARMA process the one we use for the GARCH model ?
3) Finally, according to John Hull:
"a GARCH (1,1) indicates that the conditional variance is based on the most recent observation of u(n-1)^2 and the most recent estimate of the variance rate."
So if I understand this well what is meant by "the most recent observations" are the error terms ? I find it difficult to apprehend this concept as to me the error terms can not be osberved directly.
Thanks in advance to the one(s) that will help me to clarify these points, it would help a lot :)
