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Analytical Gradients of Dynamic Conditional Correlation Models

Author

Listed:
  • Massimiliano Caporin

    (Department of Statistical Sciences, University of Padova, 35122 Padova PD, Italy)

  • Riccardo (Jack) Lucchetti

    (DISES, Università Politecnica delle Marche, 60121 Ancona AN, Italy)

  • Giulio Palomba

    (DISES, Università Politecnica delle Marche, 60121 Ancona AN, Italy)

Abstract

We provide the analytical gradient of the full model likelihood for the Dynamic Conditional Correlation (DCC) specification by Engle (2002), the generalised version by Cappiello et al. (2006), and of the cDCC model by Aielli(2013). We discuss how the gradient might be further extended by introducing elements related to the conditional variance parameters, and discuss the issue arising from the estimation of constrained and/or reparametrised versions of the model. A computational simulation compares analytical versus numerical gradients, with a view to parameter estimation; we find that analytical differentiation yields more efficiency and improved accuracy.

Suggested Citation

  • Massimiliano Caporin & Riccardo (Jack) Lucchetti & Giulio Palomba, 2020. "Analytical Gradients of Dynamic Conditional Correlation Models," JRFM, MDPI, vol. 13(3), pages 1-21, March.
    • Handle: RePEc:gam:jjrfmx:v:13:y:2020:i:3:p:49-:d:328491
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    References listed on IDEAS

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    1. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    2. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    3. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    4. Lorenzo Cappiello & Robert F. Engle & Kevin Sheppard, 2006. "Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns," Journal of Financial Econometrics, Oxford University Press, vol. 4(4), pages 537-572.
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    8. Engle, Robert F & Sheppard, Kevin K, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series qt5s2218dp, Department of Economics, UC San Diego.
    9. Lucchetti, Riccardo, 2002. "Analytical Score for Multivariate GARCH Models," Computational Economics, Springer;Society for Computational Economics, vol. 19(2), pages 133-143, April.
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    11. Yanqin Fan & Sergio Pastorello & Eric Renault, 2015. "Maximization by parts in extremum estimation," Econometrics Journal, Royal Economic Society, vol. 18(2), pages 147-171, June.
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    Cited by:

    1. Massimiliano Caporin & Giuseppe Storti, 2020. "Financial Time Series: Methods and Models," JRFM, MDPI, vol. 13(5), pages 1-3, April.
    2. Riccardo Lucchetti & Luca Pedini, 2024. "The Spherical Parametrisation for Correlation Matrices and its Computational Advantages," Computational Economics, Springer;Society for Computational Economics, vol. 64(2), pages 1023-1046, August.

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    Keywords

    DCC; cDCC; GDCC; analytical gradient;
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