For estimating the realized volatility and
covariance by using high frequency data,
Kunitomo and Sato (2008a,b) have proposed
the Separating Information Maximum Likelihood (SIML) method
when there are micro-market noises.
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 non-Gaussian processes and volatility models.
We also show that the SIML estimator has the asymptotic robustness
in the sense that
it is consistent and it has the asymptotic normality
when
there are autocorrelations in the market noise terms
and there are endogenous correlations between
the signal and noise terms.
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