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TAIL AND NONTAIL MEMORY WITH APPLICATIONSTO EXTREME VALUE AND ROBUSTSTATISTICS

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 tocharacterize separately extremal and nonextremalinformation, including tail log-exceedances andevents, and tail-trimmed levels. We prove that nearepoch dependence (McLeish, 1975; Gallant and White,1988) andL0-approximability(Pötscher and Prucha, 1991) are equivalent for tailevents and tail-trimmed levels, ensuring a Gaussiancentral limit theory for important extreme value androbust statistics under general conditions. We applythe theory to characterize the extremal andnonextremal memory properties of possibly veryheavy-tailed GARCH processes and distributed lags.This in turn is used to verify Gaussian limits fortail index, tail dependence, and tail-trimmed sumsof these data, allowing for Gaussian asymptotics fora new tail-trimmed least squares estimator forheavy-tailed processes.

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Type
Research Article
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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 refereesand co-editor Yuichi Kitamura for helpfulsuggestions.

References

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