Estimation and empirical performance of non-scalar dynamic conditional correlation models

This paper presents a method capable of estimating richly parametrized versions of the dynamic conditional correlation (DCC) model that go beyond the standard scalar case. The algorithm is based on the maximization of a Gaussian quasi-likelihood using a Bregman-proximal trust-region method to handle the various non-linear stationarity and positivity constraints that arise in this context. We consider the general matrix Hadamard DCC model with full rank, rank equal to two and, additionally, two different rank one matrix specifications. In the last mentioned case, the elements of the vectors that determine the rank one parameter matrices are either arbitrary or parsimoniously defined using the Almon lag function. We use actual stock returns data in dimensions up to thirty in order to carry out performance comparisons according to several in- and out-of-sample criteria. Our empirical results show that the use of richly parametrized models adds value with respect to the conventional scalar case.