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April 2000 The maximum of the periodogram for a heavy-tailed sequence
Thomas Mikosch, Sidney Resnick, Gennady Samorodnitsky
Ann. Probab. 28(2): 885-908 (April 2000). DOI: 10.1214/aop/1019160264

Abstract

We consider the maximum of the periodogram based on an infinite variance heavy-tailed sequence. For $\alpha < 1$ we show that the maxima constitute a weakly convergent sequence and find its limiting distribution. For $1 \leq \alpha < 2$ we show that the sequence of the maxima is not tight and find a normalization that makes it tight.

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Thomas Mikosch. Sidney Resnick. Gennady Samorodnitsky. "The maximum of the periodogram for a heavy-tailed sequence." Ann. Probab. 28 (2) 885 - 908, April 2000. https://doi.org/10.1214/aop/1019160264

Information

Published: April 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.62097
MathSciNet: MR1782277
Digital Object Identifier: 10.1214/aop/1019160264

Subjects:
Primary: 62M15
Secondary: 60F05, 60G10, 60G55.

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 2 • April 2000
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