On Tail Index Estimation for Dependent, Heterogenous Data

Jonathan B. Hill ()

Econometrics from EconWPA

Abstract: In this paper we analyze the asymptotic properties of the popular distribution tail index estimator by B. Hill (1975) for possibly heavy- tailed, heterogenous, dependent processes. We prove the Hill estimator is weakly consistent for processes with extremes that form mixingale sequences, and asymptotically normal for processes with extremes that are near-epoch-dependent on the extremes of a mixing process. Our limit theory covers infinitely many ARFIMA and FIGARCH processes, stochastic recurrence equations, and simple bilinear processes. Moreover, we develop a simple non-parametric kernel estimator of the asymptotic variance of the Hill estimator, and prove consistency for extremal-NED processes.

Keywords: Hill estimator; regular variation; infinite variance; near epoch dependence; mixingale; kernel estimator; tail array sum. (search for similar items in EconPapers)
JEL-codes: C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2005-05-20, Revised 2006-03-24
Note: Type of Document - pdf; pages: 23
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Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpem:0505005

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