Title: The S-TSRV: Robust High Frequency Estimation
Abstract: In this paper, we derive a new algebraic property of two scales estimation in high frequency data, under which the effect of sampling times is cancelled to high order. This is a particular robustness property of the two scales construction. In general, irregular times can cause problems in estimators based on equidistant observation of (trade or quote) times.
The new algebraic property can be combined with pre-averaging, giving rise to the smoothed two-scales realized volatility (S-TSRV). We derive a finite sample solution to controlling edge effects and for handling endogenous observation times and asynchronously observed multivariate data. In connection with this development, we use the algebraic approach to define a version of the S-TSRV which has particularly small edge effect in microstructure noise. The main result of the paper is a representation of the statistical error of the estimator in terms of simple components. As an application, the paper develops a central limit theory for multivariate volatility estimators.