Localized realized volatility modeling

Abstract

With the recent availability of high-frequency financial data the long-range dependence of volatility regained researchers' interest and has led to the consideration of long-memory models for volatility. The long-range diagnosis of volatility, however, is usually stated for long sample periods, while for small sample sizes, such as one year, the volatility dynamics appears to be better described by short-memory processes. The ensemble of these seemingly contradictory phenomena point towards short-memory models of volatility with nonstationarities, such as structural breaks or regime switches, that spuriously generate a long memory pattern. In this paper we adopt this view on the dependence structure of volatility and propose a localized procedure for modeling realized volatility. That is at each point in time we determine a past interval over which volatility is approximated by a local linear process. A simulation study shows that long memory processes as well as short memory processes with structural breaks can be well approximated by this local approach. Furthermore, using S&P500 data we find that our local modeling approach outperforms long-memory type models and models with structural breaks in terms of predictability. © 2010.