This paper proposes a latent factor model with underlyingWishart distribution to
capture the dynamics of daily realized covariance matrices for forecasting purposes.
The long memory in the series is captured by means of aggregating latent factors with
stochastic volatility structure, where the factors are extracted from the commonality
in the dynamics of realized variance and covariance series. This new model accommodates
the positive-definiteness and the symmetry of variance-covariance matrix
forecasts within a very parsimonious framework with no parameter constraints. For
estimation purposes, we implement the numerical exact maximum likelihood method
on the Kitagawa state-space filtering procedure. We provide Monte Carlo evidence
on the accuracy of estimates and, on real data, we show that our model outperforms
existing ones when forecasting daily variance-covariance matrices.