On the limit behavior of the periodogram of high-frequency sampled stable CARMA processes
type: Item
instance of: scholarly article
title: On the limit behavior of the periodogram of high-frequency sampled stable CARMA processes
zbMATH Open document ID: 1275.62069
author: Vicky Fasen
author: Florian Fuchs
published in: Stochastic Processes and their Applications
publication date: 2012-11-15T00:00:00Z
review text: The aim of this paper is to investigate a sampled sequence of a casual stable CARMA process if we observe the underlying process at equidistant time points with small distances as are used for modeling high-frequency data and to study the asymptotic behavior of the sampled process in the frequency domain. As the process one considers a continuous-time ARMA process (CARMA) driven by a symmetric \(\alpha\)-stable Lévy process with positive \(\alpha\) not exceeding the upper limit 2. One investigates the normalized periodogram that converges (including its self-normalized versions) under a suitable condition on the sampling pattern to functions of stable distributions. The proofs exploit some methods from the geometry of numbers.
reviewed by: Tomáš Cipra
Mathematics Subject Classification ID: 62M15
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 6106889
zbMATH Keywords: high-frequency data
zbMATH Keywords: lattice
zbMATH Keywords: Lévy process
zbMATH Keywords: self-normalized periodogram
zbMATH Keywords: stable distributions
MaRDI profile type: Publication
full work available at URL: j.spa.2012.08.003
OpenAlex ID: W2074183973
DOI: 10.1016/J.SPA.2012.08.003
description: scientific article; zbMATH DE number 6106889