The volatility of realized volatility

Using unobservable conditional variance as measure, latentvariable approaches, such as GARCH and stochasticvolatility models, have traditionally been dominating the empirical finance literature. In recent years, with the availability of highfrequency financial market data modeling realized volatility has become a new and innovative research direction. By constructing observable or realized volatility series from intraday transaction data, the use of standard time series models, such as ARFIMA models, have become a promising strategy for modeling and predicting (daily) volatility. In this paper, we show that the residuals of the commonly used timeseries models for realized volatility exhibit nonGaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance when modeling and forecasting realized volatility. In an empirical application for S&P500 index futures we show that allowing for timevarying volatility of realized volatility leads to a substantial improvement of the models fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting.