GARMA, HAR and rules of thumb for modelling realized volatility

This paper features an analysis of the relative effectiveness, in terms of the Adjusted R-Square, of a variety of methods of modelling realized volatility (RV), namely the use of Gegenbauer processes in Auto-Regressive Moving Average format, GARMA, as opposed to Heterogenous Auto-Regressive HAR models and simple rules of thumb. The analysis is applied to two data sets that feature the RV of the S&P500 index, as sampled at 5 min intervals, provided by the OxfordMan RV database. The GARMA model does perform slightly better than the HAR model, but both models are matched by a simple rule of thumb regression model based on the application of lags of squared, cubed and quartic, demeaned daily returns.