The Annals of Probability

The maximum of the periodogram for a heavy-tailed sequence

Thomas Mikosch, Sidney Resnick, and Gennady Samorodnitsky

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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.

Article information

Ann. Probab., Volume 28, Number 2 (2000), 885-908.

First available in Project Euclid: 18 April 2002

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Zentralblatt MATH identifier

Primary: 62M15: Spectral analysis
Secondary: 60F05: Central limit and other weak theorems 60G10: Stationary processes 60G55.

Periodogram discrete Fourier transform stable random variable stable process stochastic integral infinite variance linear process point process convergence


Mikosch, Thomas; Resnick, Sidney; Samorodnitsky, Gennady. The maximum of the periodogram for a heavy-tailed sequence. Ann. Probab. 28 (2000), no. 2, 885--908. doi:10.1214/aop/1019160264.

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