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Abstract: In this paper, we consider the problem of estimating the covariation of twodiffusion processes when observations are subject to non-synchronicity.Building on recent papers \cite{Hay-Yos03, Hay-Yos04}, we derive second-orderasymptotic expansions for the distribution of the Hayashi-Yoshida estimator ina fairly general setup including random sampling schemes and non-anticipativerandom drifts. The key steps leading to our results are a second-orderdecomposition of the estimator-s distribution in the Gaussian set-up, astochastic decomposition of the estimator itself and an accurate evaluation ofthe Malliavin covariance. To give a concrete example, we compute the constantsinvolved in the resulting expansions for the particular case of sampling schemegenerated by two independent Poisson processes.



Author: Arnak Dalalyan IGM-LabInfo, Nakahiro Yoshida

Source: https://arxiv.org/







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