Estimating and Forecasting Volatility Using Leverage Effect

Abstract

This research provides a theoretical foundation for our previous empirical finding that leverage effect has a role in estimating and forecasting volatility. This empirics is also related to earlier econometric studies of news impact curves (Engle and Ng, Chen and Ghysels). Our new theoretical development is based on the concept of projection on stable subspaces of semi-martingales. We show that this projection provides a framework for forecasting (across time periods) that is internally consistent with the semi-martingale model which is used for the intra-day high frequency asymptotics. The paper shows that the approach provides improved estimation and forecasting both theoretically, in simulation, and in data.