Before revision:  We start by studying the most commonly used estimator, the realized covariance matrix {\it  (RCV)  . We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility processes not only through the underlying integrated covariance matrixSigma , but also on how the covolatility processes vary in time.
After revision:  We start by studying the most commonly used estimator, the realized covariance matrix {\it (RCV) . We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility processes not only through the underlying integrated covariance matrixSigma , but also on how the covolatility process varies in time.