The periodogram at the Fourier frequencies
type: Item
instance of: scholarly article
title: The periodogram at the Fourier frequencies
zbMATH Open document ID: 1025.62030
DOI: 10.1016/S0304-4149(99)00086-1
published in: Stochastic Processes and their Applications
publication date: 2003-11-03T00:00:00Z
review text: The authors consider an iid sequence (\(Z_t\)) of random variables with \(Z=Z_0\), \(EZ=0\) and \(EZ^2=1\). They give a review of the asymptotic properties of the periodogram ordinates of the iid sequence at the Fourier frequencies and investigate the limit behaviour of various functions of these periodogram ordinates. In some cases (extremes, point processes, empirical distribution functions) an analogy was found with an iid standard exponential sequence, whereas in other cases (empirical processes, weighted sums) the analogy failed. Periodogram ordinates of an infinite variance iid sequence were also considered.
Mathematics Subject Classification ID: 62M15
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 2000161
zbMATH Keywords: periodogram
zbMATH Keywords: Fourier frequencies
zbMATH Keywords: iid sequence
zbMATH Keywords: asymptotic normality
zbMATH Keywords: empirical process
zbMATH Keywords: point process
author: Piotr Kokoszka
author: T. Mikosch
reviewed by: Ivan Křivý
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2000161