Stock Index Volatility Forecasting with High Frequency Data

The increasing availability of financial market data at intraday frequencies has not only led to the development of improved ex-post volatility measurements but has also inspired research into their potential value as an information source for longer horizon volatility forecasts. In this paper we explore the forecasting value of these high frequency series in conjunction with a variety of volatility models for returns on the Standard & Poor's 100 stock index. We consider two so-called realised volatility models in which the cumulative squared intraday returns are modelled directly. We adopt an unobserved components model where actual volatility is modelled as an autoregressive moving average process and an autoregressive fractionally integrated moving average model which allows for long memory in the logarithms of realised volatility. We compare the predictive abilities of these realised volatility models with those of daily time-varying volatility models, such as Stochastic Volatility (SV) and Generalised Autoregressive Conditional Heteroskedasticity (GARCH) models which are both extended to include the intraday volatility measure. For forecasting horizons ranging from one day to one week the most accurate out-of-sample volatility forecasts are obtained with the realised volatility and the extended SV models; all these models contain information inherent in the high frequency returns. In the absence of the intraday volatility information, we find that the SV model outperforms the GARCH model.