For estimating the realized volatility and covariance by using high frequency data, we have introduced
the Separating Information Maximum Likelihood (SIML) method when there are possibly
micro-market noises by Kunitomo and Sato (2008a, 2008b, 2010a, 2010b). The resulting estimator
is simple and it has the representation as a specific quadratic form of returns. We show that the
SIML estimator has reasonable asymptotic properties; it is consistent and it has the asymptotic
normality (or the stable convergence in the general case) when the sample size is large under
general conditions including some non-Gaussian processes and some volatility models. Based on
simulations, we find that the SIML estimator has reasonable finite sample properties and thus it
would be useful for practice. The SIML estimator has the asymptotic robustness properties in
the sense it is consistent when the noise terms are weakly dependent and they are endogenously
correlated with the efficient market price process. We also apply our method to an analysis of
Nikkei-225 Futures, which has been the major stock index in the Japanese financial sector.
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