Kunitomo, Naoto and Hiroumi Misaki

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 estimation is useful for estimating the integrated covariance and hedging coefficient when we have micro-market noise and financial high frequency data are randomly sampled. The SIML estimation is consistent and has the stable convergence (i.e. the asymptotic normality in the deterministic case) and it has reasonable finite sample properties with these effects.