A Robust Estimation of Integrated Volatility under Round-off Errors, Micro-market Price Adjustments and Noises

For estimating the integrated volatility by using high frequency data, Kunitomo and Sato (2008, 2011, 2013) have proposed the Separating Information Maximum Likelihood (SIML) method when there are micro-market noises. The SIML estimator has reasonable nite sample properties and asymptotic properties when the sample size is large under reasonable conditions. We show that the SIML estimator has the robustness properties in the sense that it is consistent and has the stable convergence (i.e. the asymptotic normality in the deterministic case) when there are round- off errors and micro-market price adjustments and noises for the underlying (continuous time) stochastic process. The SIML estimation has also reasonable nite sample properties with these effects and dominate the existing methods such as the realized kernel method and the pre-averaging method in some situations. --