Stable limits for sums of dependent infinite variance random variables
Bartkiewicz, Katarzyna; Jakubowski, Adam; Mikosch, Thomas; Wintenberger, Olivier (2011), Stable limits for sums of dependent infinite variance random variables, Probability Theory and Related Fields, 150, 3-4, p. 337-372. 10.1007/s00440-010-0276-9
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/0906.2717v4
Journal nameProbability Theory and Related Fields
MetadataShow full item record
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.
Subjects / KeywordsStationary sequence; Stable limit distribution; Weak convergence; Mixing; Weak dependence; Characteristic function; Regular variation; GARCH; Stochastic volatility model; ARMA process
Showing items related by title and author.
The cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains Wintenberger, Olivier; Mikosch, Thomas (2014) Article accepté pour publication ou publié