Large and very large portfolios of financial assets are routine for many individuals and
organizations. The two most widely used models of conditional covariances and correlations
are BEKK and DCC. BEKK suffers from the archetypal "curse of dimensionality" whereas
DCC does not. This is a misleading interpretation of the suitability of the two models to be
used in practice. The primary purposes of the paper are to define targeting as an aid in
estimating matrices associated with large numbers of financial assets, analyze the similarities
and dissimilarities between BEKK and DCC, both with and without targeting, on the basis of
structural derivation, the analytical forms of the sufficient conditions for the existence of
moments, and the sufficient conditions for consistency and asymptotic normality, and
computational tractability for very large (that is, ultra high) numbers of financial assets, to
present a consistent two step estimation method for the DCC model, and to determine whether
BEKK or DCC should be preferred in practical applications.
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