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TAIL AND NONTAIL MEMORY WITH APPLICATIONS TO EXTREME VALUE AND ROBUST STATISTICS

Published online by Cambridge University Press:  08 March 2011

Jonathan B. Hill
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Abstract

New notions of tail and nontail dependence are used to characterize separately extremal and nonextremal information, including tail log-exceedances and events, and tail-trimmed levels. We prove that near epoch dependence (McLeish, 1975; Gallant and White, 1988) and L0-approximability (Pötscher and Prucha, 1991) are equivalent for tail events and tail-trimmed levels, ensuring a Gaussian central limit theory for important extreme value and robust statistics under general conditions. We apply the theory to characterize the extremal and nonextremal memory properties of possibly very heavy-tailed GARCH processes and distributed lags. This in turn is used to verify Gaussian limits for tail index, tail dependence, and tail-trimmed sums of these data, allowing for Gaussian asymptotics for a new tail-trimmed least squares estimator for heavy-tailed processes.

Type
Research Article
Information
Econometric Theory , Volume 27 , Issue 4 , August 2011 , pp. 844 - 884
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

The authors kindly thanks two anonymous referees and co-editor Yuichi Kitamura for helpful suggestions.

References

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