Volatility Forecasting with High Frequency Data

The daily volatility is typically unobserved but can be estimated using high frequent tick-by-tick data. In this paper, we study the problem of forecasting the unobserved volatility using past values of measured volatility. Specifically, we use daily estimates of volatility based on high frequency data, called realized variance, and construct the optimal linear forecast of future volatility. Utilizing single exponential smoothing, we develop formulae that yield the optimal coefficients for our forecast. We compare the precision of our forecast with those of two popular forecasting models, the HAR regression model and the Local Level model, in terms of mean squared errors. In empirical analysis of the seven DJIA stocks, our model performs better than two competing models in most of the cases.