The maximum of the periodogram for a heavy-tailed sequence
Thomas Mikosch, Sidney I. Resnick, Gennady Pinkhosovich Samorodnitsky · The Annals of Probability · 2000
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.