Threshold Bipower Variation and the Impact of Jumps on Volatility Forecasting

Abstract

This study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility. This result becomes apparent once volatility is correctly separated into its continuous and discontinuous component. To this purpose, we introduce the concept of threshold bipower variation, which is based on the joint use of bipower variation and threshold estimation. We show that its generalization (threshold multipower variation) admits a feasible central limit theorem in the presence of jumps, which is not attainable for standard multipower variation if not in very restrictive cases. Importantly, with respect to the standard multipower variation, our estimator provides less biased estimates of the continuous quadratic variation and jumps in finite samples. It also provides a new test for jump detection which has substantially more power than previous tests. Empirical analysis (on the S&P500 index, single stocks and US bond yields) shows that the proposed techniques improve significantly the accuracy of volatility forecasts especially in periods following the occurrence of a jump.

Keywords: volatility, forecasting, jumps, HAR