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.
Publié le : 2000-04-14
Classification:
Periodogram,
discrete Fourier transform,
stable random variable,
stable process,
stochastic integral,
infinite variance,
linear process,
point process convergence,
62M15,
60F05,
60G10,
60G55.
@article{1019160264,
author = {Mikosch, Thomas and Resnick, Sidney and Samorodnitsky, Gennady},
title = {The maximum of the periodogram for a heavy-tailed sequence},
journal = {Ann. Probab.},
volume = {28},
number = {1},
year = {2000},
pages = { 885-908},
language = {en},
url = {http://dml.mathdoc.fr/item/1019160264}
}
Mikosch, Thomas; Resnick, Sidney; Samorodnitsky, Gennady. The maximum of the periodogram for a heavy-tailed sequence. Ann. Probab., Tome 28 (2000) no. 1, pp. 885-908. http://gdmltest.u-ga.fr/item/1019160264/