Tail index of an ar(1) model with arch(1) errors

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)920-940
Journal / PublicationEconometric Theory
Volume29
Issue number5
Publication statusPublished - Oct 2013
Externally publishedYes

Abstract

Relevant sample quantities such as the sample autocorrelation function and extremes contain useful information about autoregressive time series with heteroskedastic errors. As these quantities usually depend on the tail index of the underlying heteroskedastic time series, estimating the tail index becomes an important task. Since the tail index of such a model is determined by a moment equation, one can estimate the underlying tail index by solving the sample moment equation with the unknown parameters being replaced by their quasi-maximum likelihood estimates. To construct a confidence interval for the tail index, one needs to estimate the complicated asymptotic variance of the tail index estimator, however. In this paper the asymptotic normality of the tail index estimator is first derived, and a profile empirical likelihood method to construct a confidence interval for the tail index is then proposed. A simulation study shows that the proposed empirical likelihood method works better than the bootstrap method in terms of coverage accuracy, especially when the process is nearly nonstationary. © 2013 Cambridge University Press.

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Citation Format(s)

Tail index of an ar(1) model with arch(1) errors. / Chan, Ngai Hang; Li, Deyuan; Peng, Liang et al.
In: Econometric Theory, Vol. 29, No. 5, 10.2013, p. 920-940.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review