  This paper presents a central limit theorem for a pre-averaged version of the
realized covariance estimator for the quadratic covariation of a discretely
observed semimartingale with noise. The semimartingale possibly has jumps,
while the observation times show irregularity, non-synchronicity, and some
dependence on the observed process. It is shown that the observation times'
effect on the asymptotic distribution of the estimator is only through two
characteristics: the observation frequency and the covariance structure of the
noise. This is completely different from the case of the realized covariance in
a pure semimartingale setting.
