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

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  • Massimiliano Caporin

    ()
    (Department of Economic Sciences University of Padova)

  • Michael McAleer

    (Universidad Complutense de Madrid.Department of Quantitative Economics)

Abstract

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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Bibliographic Info

Paper provided by Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico in its series Documentos de Trabajo del ICAE with number 0904.

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Length: 26 pages
Date of creation: 2009
Date of revision:
Handle: RePEc:ucm:doicae:0904

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Related research

Keywords: Conditional correlations; Conditional covariances; Diagonal models; Forecasting; Generalized models; Hadamard models; Scalar models; Targeting.;

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  1. Neil Shephard & Kevin Sheppard & Robert F. Engle, 2008. "Fitting vast dimensional time-varying covariance models," Economics Series Working Papers 403, University of Oxford, Department of Economics.
  2. Billio, Monica & Caporin, Massimiliano, 2009. "A generalized Dynamic Conditional Correlation model for portfolio risk evaluation," Mathematics and Computers in Simulation (MATCOM), Elsevier, Elsevier, vol. 79(8), pages 2566-2578.
  3. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
  4. Matteo Bonato & Massimiliano Caporin & Angelo Ranaldo, 2009. "Forecasting realized (co)variances with a block structure Wishart autoregressive model," Working Papers 2009-03, Swiss National Bank.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Massimiliano Caporin & Paolo Paruolo, 2009. "Structured Multivariate Volatility Models," "Marco Fanno" Working Papers 0091, Dipartimento di Scienze Economiche "Marco Fanno".
  11. Manabu Asai & Massimiliano Caporin & Michael McAleer, 2009. "Block Structure Multivariate Stochastic Volatility Models," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-699, CIRJE, Faculty of Economics, University of Tokyo.
  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. 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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