Skip to main content
Article thumbnail
Location of Repository

"Do We Really Need Both BEKK and DCC? A Tale of Two Covariance Models"

By Massimiliano Caporin and Michael McAleer


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.

OAI identifier:

Suggested articles


  1. (2009). A generalised dynamic conditional correlation model for portfolio risk evaluation,
  2. (1987). As a multivariate generalization of Tsay’s
  3. (2003). Asymptotic theory for a vector ARMA-GARCH model,
  4. (2003). Asymptotic theory for multivariate GARCH processes,
  5. (1987). Conditional heteroscedastic time series models,
  6. (2008). Consistent estimation of large scale dynamic conditional correlations,
  7. (2008). Fitting vast dimensional time-varying covariance models,
  8. (2006). Flexible dynamic conditional correlation multivariate GARCH for asset allocation,
  9. (2009). Forecasting realized (co)variances with a block structure Wishart autoregressive model,
  10. (2008). Generalized autoregressive conditional correlation, Econometric Theory,
  11. (2008). In comparison with the purported proofs of consistency and asymptotic normality of the QML estimators of the DCC parameters in the literature, McAleer et al.
  12. (1994). Large Sample Estimation and Hypothesis Testing,
  13. (1990). Modelling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH approach,
  14. (1995). Multivariate simultaneous generalized ARCH,
  15. (1992). On the relation between the expected value and volatility of the nominal excess return on stocks,
  16. (1982). Random Coefficient Autoregressive Models: An Introduction,
  17. (1998). Strong consistency of estimators for multivariate ARCH models,
  18. (2009). Structured multivariate volatility models,
  19. (2002). The author assumes “reasonable regularity conditions” and “standard regularity conditions” (p. 342), without stating them, and refers to the theoretical results in Engle and Sheppard
  20. (2001). The authors assume, but do not verify, that the standard regularity conditions required for two step GMM to yield consistent and asymptotically normal estimators, as given, for example,
  21. (2006). The authors develop an extension of the DCC model to incorporate asymmetries, but do not establish the asymptotic properties of the estimators.
  22. (2008). The authors refer to Aielli’s (2008) model and estimation method, but not to his purported proofs of consistency and asymptotic normality. Moreover, they do not refer to the main result in Aielli
  23. (2001). Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH, Working Paper 2001-15,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.