  In this paper, the estimation of the Integrated Covariance matrix from
high-frequency data, for high dimensional stock price process, is considered.
The Hayashi-Yoshida covolatility estimator is an improvement over Realized
covolatility for asynchronous data and works well in low dimensions. However it
becomes inconsistent and unreliable in the high dimensional situation. We study
the bulk spectrum of this matrix and establish its connection to the spectrum
of the true covariance matrix in the limiting case where the dimension goes to
infinity. The results are illustrated with simulation studies in finite, but
high, dimensional cases. An application to real data with tick-by-tick data on
50 stocks is presented.
