Interval estimation of the tail index of a GARCH(1,1) model
AbstractIt 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 InfoArticle provided by Springer in its journal TEST.
Volume (Year): 21 (2012)
Issue (Month): 3 (September)
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Web page: http://www.springerlink.com/link.asp?id=120411
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- 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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