Functional volatility forecasting

Widely used volatility forecasting methods are usually based on low-frequency time series models. Although some of them employ high-frequency observations, these intraday data are often summarized into low-frequency point statistics, for example, daily realized measures, before being incorporated into a forecasting model. This paper contributes to the volatility forecasting literature by instead predicting the next-period intraday volatility curve via a functional time series forecasting approach. Asymptotic theory related to the estimation of latent volatility curves via functional principal analysis is formally established, laying a solid theoretical foundation of the proposed forecasting method. In contrast with nonfunctional methods, the proposed functional approach fully exploits the rich intraday information and hence leads to more accurate volatility forecasts. This is confirmed by extensive comparisons between the proposed method and those widely used nonfunctional methods in both Monte Carlo simulations and an empirical study on a number of stocks and equity indices from the Chinese market.