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Targeting estimation of CCC-Garch models with infinite fourth moments

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  • Rasmus Søndergaard Pedersen

    (Department of Economics, Copenhagen University)

Abstract

As an alternative to quasi-maximum likelihood, targeting estimation is a much applied estimation method for univariate and multivariate GARCH models. In terms of variance targeting estimation recent research has pointed out that at least finite fourth-order moments of the data generating process is required if one wants to perform inference in GARCH models relying on asymptotic normality of the estimator, see Pedersen and Rahbek (2014) and Francq et al. (2011). Such moment conditions may not be satisfied in practice for financial returns highlighting a large drawback of variance targeting estimation. In this paper we consider the large-sample properties of the variance targeting estimator for the multivariate extended constant conditional correlation GARCH model when the distribution of the data generating process has infinite fourth moments. Using non-standard limit theory we derive new results for the estimator stating that its limiting distribution is multivariate stable. The rate of consistency of the estimator is slower than squareroot T (as obtained by the quasi-maximum likelihood estimator) and depends on the tails of the data generating process

Suggested Citation

  • Rasmus Søndergaard Pedersen, 2014. "Targeting estimation of CCC-Garch models with infinite fourth moments," Discussion Papers 14-04, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:1404
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    References listed on IDEAS

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    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. 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.
    3. Rasmus S. Pedersen & Anders Rahbek, 2014. "Multivariate variance targeting in the BEKK–GARCH model," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 24-55, February.
    4. Massimiliano Caporin & Michael McAleer, 2012. "Do We Really Need Both Bekk And Dcc? A Tale Of Two Multivariate Garch Models," Journal of Economic Surveys, Wiley Blackwell, vol. 26(4), pages 736-751, September.
    5. Jensen, Søren Tolver & Rahbek, Anders, 2004. "Asymptotic Inference For Nonstationary Garch," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1203-1226, December.
    6. 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.
    7. Christian Francq & Lajos Horváth, 2011. "Merits and Drawbacks of Variance Targeting in GARCH Models," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(4), pages 619-656.
    8. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    9. Francq, Christian & Zakoïan, Jean-Michel, 2012. "Qml Estimation Of A Class Of Multivariate Asymmetric Garch Models," Econometric Theory, Cambridge University Press, vol. 28(1), pages 179-206, February.
    10. He, Changli & Teräsvirta, Timo, 2004. "An Extended Constant Conditional Correlation Garch Model And Its Fourth-Moment Structure," Econometric Theory, Cambridge University Press, vol. 20(5), pages 904-926, October.
    11. Basrak, Bojan & Segers, Johan, 2009. "Regularly varying multivariate time series," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1055-1080, April.
    12. Kristensen, Dennis & Linton, Oliver, 2004. "03.5.2. Consistent Standard Errors for Target Variance Approach to GARCH Estimation—Solution," Econometric Theory, Cambridge University Press, vol. 20(5), pages 990-993, October.
    13. Pan, Xiaoqing & Leng, Xuan & Hu, Taizhong, 2013. "The second-order version of Karamata’s theorem with applications," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1397-1403.
    14. Fernández, Begoña & Muriel, Nelson, 2009. "Regular variation and related results for the multivariate GARCH(p,q) model with constant conditional correlations," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1538-1550, August.
    15. Sherman, Michael & Carlstein, Edward, 2004. "Confidence intervals based on estimators with unknown rates of convergence," Computational Statistics & Data Analysis, Elsevier, vol. 46(1), pages 123-139, May.
    16. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
    17. Igor Vaynman & Brendan K. Beare, 2014. "Stable Limit Theory for the Variance Targeting Estimator," Advances in Econometrics, in: Essays in Honor of Peter C. B. Phillips, volume 33, pages 639-672, Emerald Group Publishing Limited.
    18. Hafner, Christian M. & Reznikova, Olga, 2012. "On the estimation of dynamic conditional correlation models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3533-3545.
    19. 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.
    20. Starica, Catalin, 1999. "Multivariate extremes for models with constant conditional correlations," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 515-553, December.
    21. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
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    Cited by:

    1. Rasmus Pedersen & Olivier Wintenberger, 2017. "On the tail behavior of a class of multivariate conditionally heteroskedastic processes," Working Papers hal-01436267, HAL.
    2. Simon Hetland, 2020. "Spectral Targeting Estimation of $\lambda$-GARCH models," Papers 2007.02588, arXiv.org.
    3. Qi Li & Fukang Zhu, 2020. "Mean targeting estimator for the integer-valued GARCH(1, 1) model," Statistical Papers, Springer, vol. 61(2), pages 659-679, April.
    4. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.
    5. Rasmus Pedersen & Olivier Wintenberger, 2017. "On the tail behavior of a class of multivariate conditionally heteroskedastic processes," Papers 1701.05091, arXiv.org, revised Dec 2017.
    6. Pedersen, Rasmus Søndergaard, 2017. "Inference and testing on the boundary in extended constant conditional correlation GARCH models," Journal of Econometrics, Elsevier, vol. 196(1), pages 23-36.
    7. Francq, C. & Jiménez-Gamero, M.D. & Meintanis, S.G., 2017. "Tests for conditional ellipticity in multivariate GARCH models," Journal of Econometrics, Elsevier, vol. 196(2), pages 305-319.

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    More about this item

    Keywords

    Targeting; variance targeting; multivariate GARCH; constant conditional correlation; asymptotic theory; time series; multivariate regular variation; stable distributions.;
    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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