  High-frequency data observed on the prices of financial assets are commonly
modeled by diffusion processes with micro-structure noise, and realized
volatility-based methods are often used to estimate integrated volatility. For
problems involving a large number of assets, the estimation objects we face are
volatility matrices of large size. The existing volatility estimators work well
for a small number of assets but perform poorly when the number of assets is
very large. In fact, they are inconsistent when both the number, $p$, of the
assets and the average sample size, $n$, of the price data on the $p$ assets go
to infinity. This paper proposes a new type of estimators for the integrated
volatility matrix and establishes asymptotic theory for the proposed estimators
in the framework that allows both $n$ and $p$ to approach to infinity. The
theory shows that the proposed estimators achieve high convergence rates under
a sparsity assumption on the integrated volatility matrix. The numerical
studies demonstrate that the proposed estimators perform well for large $p$ and
complex price and volatility models. The proposed method is applied to real
high-frequency financial data.
