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

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  • Massimiliano Caporin

    (Dipartimento di Scienze Economiche "Marco Fanno", Universita degli Studi di Padova)

  • Michael McAleer

    (Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam and Tinbergen Institute and Center for International Research on the Japanese Economy (CIRJE), Faculty of Economics, University of Tokyo)

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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File URL: http://www.carf.e.u-tokyo.ac.jp/pdf/workingpaper/fseries/161.pdf
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Bibliographic Info

Paper provided by Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo in its series CARF F-Series with number CARF-F-156.

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Length: 30 pages
Date of creation: Aug 2009
Date of revision:
Handle: RePEc:cfi:fseres:cf156

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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. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, April.
  3. Manabu Asai & Massimiliano Caporin & Michael McAleer, 2009. "Block Structure Multivariate Stochastic Volatility Models," CIRJE F-Series CIRJE-F-699, CIRJE, Faculty of Economics, University of Tokyo.
  4. Massimiliano Caporin & Paolo Paruolo, 2009. "Structured Multivariate Volatility Models," "Marco Fanno" Working Papers 0091, Dipartimento di Scienze Economiche "Marco Fanno".
  5. Monica Billio & Massimiliano Caporin, 2006. "A generalized Dynamic Conditional Correlation Model for Portfolio Risk Evaluation," Working Papers 2006_53, Department of Economics, University of Venice "Ca' Foscari".
  6. 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.
  7. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
  8. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
  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, vol. 2(2), pages 123-130, March.
  10. 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.
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