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An adaptive optimal estimate of the tail index for MA(1) time series

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Author Info
J.L. Geluk ()
L. Peng () (FEW-Econometrie en besliskunde)
Abstract

For samples of random variables with a regularly varying tail estimating the tail index has received much attention recently. For the proof of asymptotic normality of the tail index estimator second order regular variation is needed. In this paper we first supplement earlier results on convolution given by Geluk et al. (1997). Secondly we propose a simple estimator of the tail index for finite moving average time series. We also give a subsampling procedure in order to estimate the optimal sample fraction in the sense of minimal mean squared error.

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File URL: http://www.eur.nl/WebDOC/doc/econometrie/feweco19990330164554.ps
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Paper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number 109.

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Date of creation: 1999
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Handle: RePEc:dgr:eureir:1999109

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Related research
Keywords: optimal estimate MA(1) time series;

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  1. Somnath Datta & William McCormick, 1998. "Inference for the Tail Parameters of a Linear Process with Heavy Tail Innovations," Annals of the Institute of Statistical Mathematics, Springer, vol. 50(2), pages 337-359, June. [Downloadable!] (restricted)
  2. Dekkers, A. L. M. & Dehaan, L., 1993. "Optimal Choice of Sample Fraction in Extreme-Value Estimation," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 173-195, November. [Downloadable!] (restricted)
  3. L. de Haan & T. Themido Pereira, 1997. "Estimating the Index of a Stable Distribution," Tinbergen Institute Discussion Papers 97-040/4, Tinbergen Institute.
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