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

Rongmao Zhang, Chenxue Li and Liang Peng

Econometric Reviews, 2019, vol. 38, issue 2, 151-169

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.

Date: 2019
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DOI: 10.1080/07474938.2016.1224024

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