Efficient multipowers

Abstract

We show how to minimize the asymptotic variance of multipower estimators using a linear combination of optimal powers. Taking advantage of the lower variance provided by this technique allows to build superior estimators of integrated volatility powers. In particular, we focus on a new efficient quarticity estimator and we show, using simulated data, that we can drastically reduce the mean square error of traditional estimators. The implementation on US stock prices corroborates our theoretical findings and further shows that ecient quarticity noticeably reduces the number of detected jumps, and improves the quality of volatility forecasts.