On robust properties of the SIML estimation of volatility under micro-market noise and random sampling

For estimating the integrated volatility and covariance by using high frequency data, Kunitomo and Sato (2008, 2011) have proposed the Separating Information Maximum Likelihood (SIML) method when there are micro-market noises. The SIML estimator has reasonable finite sample properties and asymptotic properties when the sample size is large under general conditions with non-Gaussian processes or volatility models. We shall show that the SIML estimator has the asymptotic robustness property in the sense that it is consistent and has the stable convergence (i.e. the asymptotic normality in the deterministic case) as well as reasonable finite sample properties when there are micro-market noises and the observed high-frequency data are sampled randomly with the underlying (continuous time) stochastic process. We also discuss some implications of our results on public policy and risk managements in financial markets.