Efficient Multipowers

Multipower estimators, widespread for their robustness to the presence of jumps, are also useful for reducing the estimation error of integrated volatility powers even in the absence of jumps. Optimizing linear combinations of multipowers can indeed drastically reduce the variance with respect to traditional estimators. In the case of quarticity, we also prove that the optimal combination is a nearly efficient estimator, being arbitrarily close to the nonparametric efficiency bound as the number of consecutive returns employed diverges. We provide guidance on how to select the optimal number of consecutive returns to minimize mean square error. The implementation on U.S. stock prices corroborates our theoretical findings and further shows that our proposed quarticity estimator noticeably reduces the number of detected jumps, and improves the quality of volatility forecasts.