• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

Stable limits for sums of dependent infinite variance random variables

Thumbnail
Date
2011
Link to item file
https://arxiv.org/abs/0906.2717v4
Dewey
Probabilités et mathématiques appliquées
Sujet
Stationary sequence; Stable limit distribution; Weak convergence; Mixing; Weak dependence; Characteristic function; Regular variation; GARCH; Stochastic volatility model; ARMA process
Journal issue
Probability Theory and Related Fields
Volume
150
Number
3-4
Publication date
2011
Article pages
337-372
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00440-010-0276-9
URI
https://basepub.dauphine.fr/handle/123456789/16394
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Bartkiewicz, Katarzyna
Jakubowski, Adam
Mikosch, Thomas
Wintenberger, Olivier
Type
Article accepté pour publication ou publié
Abstract (EN)
The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to hold are known in the literature. However, most of these results are qualitative in the sense that the parameters of the limit distribution are expressed in terms of some limiting point process. In this paper we will be able to determine the parameters of the limiting stable distribution in terms of some tail characteristics of the underlying stationary sequence. We will apply our results to some standard time series models, including the GARCH(1, 1) process and its squares, the stochastic volatility models and solutions to stochastic recurrence equations.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.