The maximum of the periodogram for a heavy-tailed sequence

Authors
Mikosch, T Resnick, S Samorodnitsky, G
Citation
T. Mikosch et al., The maximum of the periodogram for a heavy-tailed sequence, ANN PROBAB, 28(2), 2000, pp. 885-908
Citations number
18
Categorie Soggetti
Mathematics
Journal title
ANNALS OF PROBABILITY
ISSN journal
00911798 → ACNP
Volume
28
Issue
2
Year of publication
2000
Pages
885 - 908
Database
ISI
SICI code
0091-1798(200004)28:2<885:TMOTPF>2.0.ZU;2-Z
Abstract
We consider the maximum of the periodogram based on an infinite variance he avy-tailed sequence. For alpha < 1 we show that the maxima constitute a wea kly convergent sequence and find its limiting distribution. For 1 <less tha n or equal to> alpha < 2 we show that the sequence of the maxima is not tig ht and find a normalization that makes it tight.