  Estimation of high dimensional covariance matrices is an interesting and
important research topic. In this paper, we propose a dynamic structure and
develop an estimation procedure for high dimensional covariance matrices.
Asymptotic properties are derived to justify the estimation procedure and
simulation studies are conducted to demonstrate its performance when the sample
size is finite. By exploring a financial application, an empirical study shows
that portfolio allocation based on dynamic high dimensional covariance matrices
can significantly outperform the market from 1995 to 2014. Our proposed method
also outperforms portfolio allocation based on the sample covariance matrix and
the portfolio allocation proposed in Fan, Fan and Lv (2008).
