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

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  • Caporin, M.
  • McAleer, M.J.

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.

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Paper provided by Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute in its series Econometric Institute Research Papers with number EI 2010-13.

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Date of creation: 23 Feb 2010
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Handle: RePEc:ems:eureir:18252

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Keywords: Hadamard models; conditional correlations; conditional covariances; diagonal models; forecasting; generalized models; scalar models; targeting;

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  1. Massimiliano Caporin & Michael McAleer, 2009. "Do We Really Need Both BEKK and DCC? A Tale of Two Covariance Models," Documentos de Trabajo del ICAE, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico 0904, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  2. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH," NBER Working Papers 8554, National Bureau of Economic Research, Inc.
  3. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 14(01), pages 70-86, February.
  4. Sheppard, Kevin & Cappiello, Lorenzo & Engle, Robert F., 2003. "Asymmetric dynamics in the correlations of global equity and bond returns," Working Paper Series, European Central Bank 0204, European Central Bank.
  5. Robert Engle & Neil Shephard & Kevin Shepphard, 2008. "Fitting vast dimensional time-varying covariance models," OFRC Working Papers Series, Oxford Financial Research Centre 2008fe30, Oxford Financial Research Centre.
  6. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 19(02), pages 280-310, April.
  7. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(3), pages 339-50, July.
  8. McAleer, Michael & Chan, Felix & Hoti, Suhejla & Lieberman, Offer, 2008. "Generalized Autoregressive Conditional Correlation," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 24(06), pages 1554-1583, December.
  9. Monica Billio & Massimiliano Caporin & Michele Gobbo, 2006. "Flexible Dynamic Conditional Correlation multivariate GARCH models for asset allocation," Applied Financial Economics Letters, Taylor and Francis Journals, Taylor and Francis Journals, vol. 2(2), pages 123-130, March.
  10. Massimiliano Caporin & Paolo Paruolo, 2009. "Structured Multivariate Volatility Models," "Marco Fanno" Working Papers, Dipartimento di Scienze Economiche "Marco Fanno" 0091, Dipartimento di Scienze Economiche "Marco Fanno".
  11. Massimiliano Caporin & Michael McAleer, 2008. "Scalar BEKK and indirect DCC," Journal of Forecasting, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 27(6), pages 537-549.
  12. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 11(01), pages 122-150, February.
  13. Hafner, Christian M. & Preminger, Arie, 2009. "On asymptotic theory for multivariate GARCH models," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 100(9), pages 2044-2054, October.
  14. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 84(1), pages 61-84, January.
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