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Inference for the tail index of a GARCH(1,1) model and an AR(1) model with ARCH(1) errors

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  • Rongmao Zhang
  • Chenxue Li
  • Liang Peng

Abstract

For a GARCH(1,1) sequence or an AR(1) model with ARCH(1) errors, one can estimate the tail index by solving an estimating equation with unknown parameters replaced by the quasi maximum likelihood estimation, and a profile empirical likelihood method can be employed to effectively construct a confidence interval for the tail index. However, this requires that the errors of such a model have at least a finite fourth moment. In this article, we show that the finite fourth moment can be relaxed by employing a least absolute deviations estimate for the unknown parameters by noting that the estimating equation for determining the tail index is invariant to a scale transformation of the underlying model.

Suggested Citation

  • Rongmao Zhang & Chenxue Li & Liang Peng, 2019. "Inference for the tail index of a GARCH(1,1) model and an AR(1) model with ARCH(1) errors," Econometric Reviews, Taylor & Francis Journals, vol. 38(2), pages 151-169, February.
    • Handle: RePEc:taf:emetrv:v:38:y:2019:i:2:p:151-169
    DOI: 10.1080/07474938.2016.1224024
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    Cited by:

    1. León, Ángel & Ñíguez, Trino-Manuel, 2020. "Modeling asset returns under time-varying semi-nonparametric distributions," Journal of Banking & Finance, Elsevier, vol. 118(C).
    2. Francq, Christian & Zakoian, Jean-Michel, 2021. "Testing the existence of moments and estimating the tail index of augmented garch processes," MPRA Paper 110511, University Library of Munich, Germany.
    3. León, Ángel & Ñíguez, Trino-Manuel, 2021. "The transformed Gram Charlier distribution: Parametric properties and financial risk applications," Journal of Empirical Finance, Elsevier, vol. 63(C), pages 323-349.

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