Do We Really Need Both BEKK and DCC? A Tale of Two Multivariate GARCH Models

Discussion Papers are a series of manuscripts in their draft form. They are not intended for circulation or distribution except as indicated by the author. For that reason Discussion Papers may not be reproduced or distributed without the written consent of the author. for financial support. This is an abridged and revised version of a paper entitled " Do we really need both BEKK and DCC? A tale of two covariance models ". Abstract The management and monitoring of very large portfolios of financial assets are routine for many individuals and organizations. The two most widely used models of conditional covariances and correlations in the class of multivariate GARCH models are BEKK and DCC. It is well known that BEKK suffers from the archetypal " curse of dimensionality " , whereas DCC does not. It is argued in this paper that this is a misleading interpretation of the suitability of the two models for use in practice. The primary purpose of this paper is to analyze the similarities and dissimilarities between BEKK and DCC, both with and without targeting, on the basis of the structural derivation of the models, the availability of analytical forms for the sufficient conditions for existence of moments, sufficient conditions for consistency and asymptotic normality of the appropriate estimators, and computational tractability for ultra large numbers of financial assets. Based on theoretical considerations, the paper sheds light on how to discriminate between BEKK and DCC in practical applications.