A dynamic component model for forecasting high-dimensional realized covariance matrices

The Multiplicative MIDAS Realized DCC (MMReDCC) model of Bauwens et al. [5] decomposes the dynamics of the realized covariance matrix of returns into short-run transitory and long-run secular components where the latter reflects the effect of the continuously changing economic conditions. The model allows to obtain positive-definite forecasts of the realized covariance matrices but, due to the high number of parameters involved, estimation becomes unfeasible for large cross-sectional dimensions. Our contribution in this paper is twofold. First, in order to obtain a computationally feasible estimation procedure, we propose an algorithm that relies on the maximization of an iteratively re-computed moment-based profile likelihood function. We assess the finite sample properties of the proposed algorithm via a simulation study. Second, we propose a bootstrap procedure for generating multi-step ahead forecasts from the MMReDCC model. In an empirical application on realized covariance matrices for fifty equities, we find that the MMReDCC not only statistically outperforms the selected benchmarks in-sample, but also improves the out-of-sample ability to generate accurate multi-step ahead forecasts of the realized covariances.