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Interval estimation of the tail index of a GARCH(1,1) model

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  • Ngai Chan
  • Liang Peng
  • Rongmao Zhang

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    Abstract

    It is known that the tail index of a GARCH model is determined by a moment equation, which involves the underlying unknown parameters of the model. A tail index estimator can therefore be constructed by solving the sample moment equation with the unknown parameters being replaced by its quasi-maximum likelihood estimates (QMLE). To construct a confidence interval for the tail index, one needs to estimate the non-trivial asymptotic variance of the QMLE. In this paper, an empirical likelihood method is proposed for interval estimation of the tail index. One advantage of the proposed method is that interval estimation can still be achieved without having to estimate the complicated asymptotic variance. A simulation study confirms the advantage of the proposed method. Copyright Sociedad de Estadística e Investigación Operativa 2012

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    Bibliographic Info

    Article provided by Springer in its journal TEST.

    Volume (Year): 21 (2012)
    Issue (Month): 3 (September)
    Pages: 546-565

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    Handle: RePEc:spr:testjl:v:21:y:2012:i:3:p:546-565

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    Related research

    Keywords: Empirical likelihood; GARCH model; Tail index; 62M10; 62E20; 60F17;

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    References

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    1. Song Chen & Ingrid Van Keilegom, 2009. "A review on empirical likelihood methods for regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 18(3), pages 415-447, November.
    2. Ling, Shiqing, 2007. "Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models," Journal of Econometrics, Elsevier, vol. 140(2), pages 849-873, October.
    3. Quintos, Carmela & Fan, Zhenhong & Phillips, Peter C B, 2001. "Structural Change Tests in Tail Behaviour and the Asian Crisis," Review of Economic Studies, Wiley Blackwell, vol. 68(3), pages 633-63, July.
    4. Song Chen & Ingrid Van Keilegom, 2009. "Rejoinder on: A review on empirical likelihood methods for regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 18(3), pages 468-474, November.
    5. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
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    Cited by:
    1. Sun, Haoze & Jiang, Yuexiang, 2014. "Empirical likelihood based confidence intervals for the tail index when γ<−1/2," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 149-157.

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