Microstructure noise in the continuous case: Approximate efficiency of the adaptive pre-averaging method

This paper introduces adaptiveness to the non-parametric estimation of volatility in high frequency data. We consider general continuous Itô processes contaminated by microstructure noise. In the context of pre-averaging, we show that this device gives rise to estimators that are within 7% of the commonly conjectured “quasi-lower bound” for asymptotic efficiency. The asymptotic variance is of the form constant × bound, where the constant does not depend on the process to be estimated. The results hold with mild assumptions on the noise, and extend to mildly irregular observations.