MEM or/and LogARMA : which model for realized volatility?

There coexist two popular autoregressive conditional density model classes for series of positive financial variables such as realized volatility. One is a class of multiplicative error models (MEM), where the conditional mean is modelled autoregressively, while the specified shape of conditional distribution imposes evolution on higher order moments. The other class contains LogARMA models – ARMA models for logarithms of the original series, with a possibly time varying conditional distribution imposed on top of it. For MEM models, generating forecasts is straightforward, while for LogARMA models, additional numerical integration may be required. We compare small and big models from the two classes, along with their combinations, in terms of in-sample fit and out-of-sample predictability, using real data on realized volatility. The forecast combination weights show that both model classes are able to generate competitive forecasts, but the class of LogARMA models appears more reliable in forecasting than the class of MEM models