S&P500 volatility analysis using high-frequency multipower variation volatility proxies

Seasonality often exists in high-frequency intraday return, however, not for the intraday quadratic variation. To the authors’ best knowledge, there are two important literatures Taylor and Xu (1997) and Martens et al. (2002) dealing with seasonality in high-frequency intraday return. For better forecasts, Taylor and Xu (1997) suggested to use variance multiplier to deseasonalize the intraday return (one-minute data) for FOREX in a GARCH-based model. Similar approached had been implemented by Martens et al. (2002) in spot FOREX (hourly data) of the Deutsche mark and the Japanese yen against the US dollar. From the authors point of views, since the GARCH model specifications consist of conditional mean (return) and conditional volatility equations, the intraday returns have direct impact to the volatility estimation accuracy. However, for high-frequency volatility models such as HAR and ARFIMA, these models directly using the realized volatility (or other power variation volatility) which have no direct influences from the intraday return.

Other than GARCH-based models, Deo et al. (2006) proposed a slow time-varying seasonal intraday return filtration (hourly data) for the US stock market using stochastic volatility model. Ghysels et al. (2006) suggested mix data sampling (MIDAS) regression approach with the consideration of seasonal adjustment in S&P500 index empirical analysis. As a summary, the intraday return seasonality filtration can be considered as a special topic which needs a careful study in terms of their theoretical properties. Thus, the authors only have intension to include this feature in our future study.