  Modeling and forecasting covariance matrices of asset returns play a crucial
role in finance. The availability of high frequency intraday data enables the
modeling of the realized covariance matrix directly. However, most models in
the literature suffer from the curse of dimensionality. To solve the problem,
we propose a factor model with a diagonal CAW model for the factor realized
covariance matrices. Asymptotic theory is derived for the estimated parameters.
In an extensive empirical analysis, we find that the number of parameters can
be reduced significantly. Furthermore, the proposed model maintains a
comparable performance with a benchmark vector autoregressive model.
