I apologise, if these question are trivial, but I am currently trying to estimate a family of GARCH models for a selection of return series as part of an undergraduate project for which I am having to do a fair amount of self-teaching.
I am following the instruction given in Tsay: Analysis of Financial Time series and upon finding the expected ARCH effects using LM/LB tests, would now like to proceed estimating the models.
However, I am having difficulties selecting the order of the mean equation, which I assume to be some form of ARMA model. Given that the mean equation and GARCH model should be jointly estimated, how do I go ahead selecting the order of the mean equation?
Tsay suggests the typical Box-Jenkins methodology of either using AIC/BIC/AICc or PACF plots when building an ARMA model, however, I believe this would lead to a sequential estimation process, based upon wrong assumptions, as volatility is not constant over time.
Do I estimate (for instance) 25 different ARMA(p,q)-GARCH(1,1) models and compare their AIC/AICc/BIC or how would I go ahead selecting the mean equation?
Furthermore, is there a package in R that gives me a series of one-day ahead forecasts of volatility based upon previously estimated parameters?
So, given an GARCH-model that has been estimated in-sample, can I use the in-sample coefficients to predict one-day ahead forecasts out-of-sample?
I luckily have a series of Realised Variance to work with when comparing the models.