I am trying to model financial data using GARCH($p$,$q$). My question is, what information criteria do I use to determine which orders for $p$ and $q$ are most suitable? For instance, for ARIMA models, one can use AIC or BIC.
Are there any ICs for GARCH models? If so, what are they? If not, what can I use to pick the most suitable GARCH model for my data?
As an aside, How can I determine this in R?
Best Answer
You can use AIC and BIC for GARCH models just as you use them for ARIMA models. You may compare the AICs or the BICs as long as your dependent variable is the same across models. In case of ARIMA that excludes comparisons between models with different order of integration; in pure GARCH this is not a problem (but it would be in ARIMA-GARCH). AICs and BICs are not comparable between models for different time series such as log-returns on S&P500 versus log-returns on Apple share price.
Information criteria are available as the standard output of GARCH model estimation in the package "rugarch" in R. There is also a special function
infocriteriathat extracts the information criteria from a fitted GARCH model of the classuGARCHfit.