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Multivariate Variance Targeting in the BEKK-GARCH Model

Author

Listed:
  • Rasmus Søndergaard Pedersen

    (University of Copenhagen)

  • Anders Rahbek

    (University of Copenhagen and CREATES)

Abstract
This paper considers asymptotic inference in the multivariate BEKK model based on (co-)variance targeting (VT). By defi?nition the VT estimator is a two-step estimator and the theory presented is based on expansions of the modifi?ed likelihood function, or estimating function, corresponding to these two steps. Strong consistency is established under weak moment conditions, while sixth order moment restrictions are imposed to establish asymptotic normality. Included simulations indicate that the multivariately induced higher-order moment constraints are indeed necessary.

Suggested Citation

  • Rasmus Søndergaard Pedersen & Anders Rahbek, 2012. "Multivariate Variance Targeting in the BEKK-GARCH Model," CREATES Research Papers 2012-53, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2012-53
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    References listed on IDEAS

    as
    1. Sébastien Laurent & Jeroen V. K. Rombouts & Francesco Violante, 2012. "On the forecasting accuracy of multivariate GARCH models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 934-955, September.
    2. Noureldin, Diaa & Shephard, Neil & Sheppard, Kevin, 2014. "Multivariate rotated ARCH models," Journal of Econometrics, Elsevier, vol. 179(1), pages 16-30.
    3. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    4. Silvennoinen, Annastiina & Teräsvirta, Timo, 2007. "Multivariate GARCH models," SSE/EFI Working Paper Series in Economics and Finance 669, Stockholm School of Economics, revised 18 Jan 2008.
    5. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    6. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    7. Francq, Christian & Zakoian, Jean-Michel, 2010. "QML estimation of a class of multivariate GARCH models without moment conditions on the observed process," MPRA Paper 20779, University Library of Munich, Germany.
    8. Christian Francq & Lajos Horváth, 2011. "Merits and Drawbacks of Variance Targeting in GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 9(4), pages 619-656.
    9. Jensen, Søren Tolver & Rahbek, Anders, 2004. "Asymptotic Inference For Nonstationary Garch," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1203-1226, December.
    10. Avarucci, Marco & Beutner, Eric & Zaffaroni, Paolo, 2013. "On Moment Conditions For Quasi-Maximum Likelihood Estimation Of Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 29(3), pages 545-566, June.
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    12. Frédérique Bec & Anders Rahbek, 2004. "Vector equilibrium correction models with non-linear discontinuous adjustments," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 628-651, December.
    13. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
    14. Boussama, Farid & Fuchs, Florian & Stelzer, Robert, 2011. "Stationarity and geometric ergodicity of BEKK multivariate GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2331-2360, October.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Covariance targeting; Variance targeting; Multivariate GARCH; BEKK; Asymptotic theory; Time series.;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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