A Component Multiplicative Error Model for Realized Volatility Measures

We propose a component Multiplicative Error Model (MEM) for modelling and forecasting realized volatility measures. In contrast to conventional MEMs, the proposed specification resorts to the use of a multiplicative component structure in order to parsimoniously parameterize the complex dependence structure of realized volatility measures. The long-run component is defined as a linear combination of MIDAS filters moving at different frequencies, while the short-run component is constrained to follow a unit mean GARCH recursion. This particular specification of the long-run component allows to reproduce very persistent oscillations of the conditional mean of the volatility process, in the spirit of Corsi's Heterogeneous Autoregressive Model (HAR). The empirical performances of the proposed model are assessed by means of an application to the realized volatility of the S&P 500 index.