  Due to the mechanism of recording, the presence of multiple transactions at
each recording time becomes a common feature for high-frequency data in
financial market. Using random matrix theory, this paper considers the
estimation of integrated covariance (ICV) matrices of high-dimensional
diffusion processes based on multiple high-frequency observations. We start by
studying the estimator, the time-variation adjusted realized covariance (TVA)
matrix, proposed in Zheng and Li (2011) without microstructure noise. We show
that in the high-dimensional case, for a class C of diffusion processes, the
limiting spectral distribution (LSD) of averaged TVA depends not only on that
of ICV, but also on the numbers of multiple transactions at each recording
time. However, in practice, the observed prices are always contaminated by the
market microstructure noise. Thus the limiting behavior of pre-averaging
averaged TVA matrices is studied based on the noisy multiple observations. We
show that for processes in class C, the pre-averaging averaged TVA has
desirable properties that it eliminates the effects of microstructure noise and
multiple transactions, and its LSD depends solely on that of the ICV matrix.
Further, three types of nonlinear shrinkage estimators of ICV are proposed
based on high-frequency noisy multiple observations. Simulation studies support
our theoretical results and show the finite sample performance of the proposed
estimators. At last, the high-frequency portfolio strategies are evaluated
under these estimators in real data analysis.
