  Recently, inference about high-dimensional integrated covariance matrices
(ICVs) based on noisy high-frequency data has emerged as a challenging problem.
In the literature, a pre-averaging estimator (PA-RCov) is proposed to deal with
the microstructure noise. Using the large-dimensional random matrix theory, it
has been established that the eigenvalue distribution of the PA-RCov matrix is
intimately linked to that of the ICV through the Marcenko-Pastur equation.
Consequently, the spectrum of the ICV can be inferred from that of the PA-RCov.
However, extensive data analyses demonstrate that the spectrum of the PA-RCov
is spiked, that is, a few large eigenvalues (spikes) stay away from the others
which form a rather continuous distribution with a density function (bulk).
Therefore, any inference on the ICVs must take into account this spiked
structure. As a methodological contribution, we propose a spiked model for the
ICVs where spikes can be inferred from those of the available PA-RCov matrices.
The consistency of the inference procedure is established and is checked by
extensive simulation studies. In addition, we apply our method to the real data
from the US and Hong Kong markets. It is found that our model clearly
outperforms the existing one in predicting the existence of spikes and in
mimicking the empirical PA-RCov matrices.
