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

• Ngai Hang Chan ^[1] ; Liang Peng ^[2] ; Rongmao Zhang ^[3]
  1. [1] Chinese University of Hong Kong

     Chinese University of Hong Kong

     RAE de Hong Kong (China)

     
  2. [2] Georgia Institute of Technology

     Georgia Institute of Technology

     Estados Unidos

     
  3. [3] Zhejiang University

     Zhejiang University

     China

     

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• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 21, Nº. 3, 2012, págs. 546-565
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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