The cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains

Wintenberger, Olivier; Mikosch, Thomas

Wintenberger, Olivier; Mikosch, Thomas (2014), The cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains, Probability Theory and Related Fields, 159, 1-2, p. 157-196. http://dx.doi.org/10.1007/s00440-013-0504-1

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00806306

Date

2014

Journal name

Probability Theory and Related Fields

Volume

159

Number

1-2

Publisher

Springer

Pages

157-196

Abstract (EN)

We introduce the cluster index of a multivariate regularly varying stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums of regularly varying sequences. We illustrate the use of the cluster index by characterizing infinite variance stable limit distributions and precise large deviation results for sums of multivariate functions acting on a stationary Markov chain under a drift condition.

Subjects / Keywords

GARCH; large deviation principle; central limit theorem; regular variation; Markov processes