Estimation and Empirical Performance of Non-Scalar DCC Models

Bauwens, Luc [UCL] Grigoryeva, Lyudmila [LaboratoiredeMathématiquesdeBesabcon,UniversitédeFranche-Comté,Besancon] Ortega, Juan-Pablo [LaboratoiredeMathématiquesdeBesabcon,UniversitédeFranche-Comté,Besancon-CentreNationaldelaRechercheScientifique,France]

A method capable of estimating richly parametrized versions of the dynamic conditional correlation(DCC)model that go beyond the standard scalar case is presented.The algorithm is based on the maximization of a Gaussian quasi-likelihood using a Bregman-proximal trust-region method that handles the various non-linear stationarity and positivity con- straints that arise in this context.Theg eneral matrix Hadamard DCC model with full rank, rank equal to two and,additionally,two different rank one matrix specifications are con- sidered. 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. Actual stock returns data in dimensions up to thirty are used in order to carry out performance comparisons according to several in-and out-of-sample criteria. Empiri- cal results show that the use of richly parametrized models adds value with respect to the conventional scalar case.