On truncated multi-power estimator of integrated volatility with noisy high frequency data

Abstract

This paper develops the asymptotic theory of the threshold pre-averaged multi-power variation estimation in the simultaneous presence of jumps and market microstructure noise and then proposes an improved estimator for integrated volatility of an Ito semi-martingale based on the obtained theory. This new class of estimation is based on the joint use of pre-averaging multi-power variation estimation in a noisy diffusion setting and the threshold technique, which serve to remove microstructure noise and jumps, respectively. Asymptotic properties of the proposed integrated volatility estimator, such as consistency and associated central limit theorems are also provided. Monte Carlo simulations show that the estimator is robust to both Levy jumps and microstructure noise and it provides less biased estimation, compared to existing estimators, of the continuous variation in finite samples. We also apply our estimator to some real high frequency financial data-sets.