Score-driven models for realized volatility

This paper sets up a statistical framework for modeling realized volatility (RV) using a Dynamic Conditional Score (DCS) model. It first shows how, for a dataset on stock indices, a preliminary analysis of RV, based on fitting a linear Gaussian model to its logarithm, suggests the use of a two component dynamic specification. It also indicates a departure from normality, a weekly pattern in the data and the presence of heteroscedasticity. Fitting the two component DCS specification with leverage and a day of the week effect is then carried out directly on RV with a Generalized Beta of the Second Kind (GB2) conditional distribution or, equivalently, on the logarithm of RV with an Exponential Generalized Beta of the Second Kind (EGB2) distribution. The forecasting performance of this model, with and without heteroscedasticity, is compared with that of the Heterogeneous Autoregression (HAR), some extensions of it and some other models. Overall there is a clear gain from using the GB2-DCS model, even when the HAR model uses additional information, such as realized semi-variance. When the aim is to forecast tail behavior, the fat-tailed GB2 model performs much better than models with thin-tailed distributions. A further exercise uses a dataset on exchange rates to compare GB2-DCS models with models that use realized quarticity. Again the additional information offers no forecasting advantage. Overall the GB2-DCS models are transparent, provide a comprehensive description of the properties of RV, and are difficult to beat for forecasting.