Information criteria for GARCH model selection

In this paper, a set of appropriately modified information criteria for selection of models from the AR-GARCH class is derived. It is argued that unmodified or naively modified traditional information criteria cannot be used for order determination in the context of conditionally heteroscedastic models. The models selected using the modified criteria are then used to forecast both the conditional mean and the conditional variance of two high frequency exchange rate series. The analysis indicates that although the use of such model selection methods does lead to significantly improved forecasting accuracies for the conditional variance in some instances, these improvements are by no means universal. The use of these criteria to jointly select conditional mean and conditional variance model orders leads to performance degradation for the conditional mean forecasts compared to models which do not allow for the heteroscedasticity.