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Absolute regularity of semi-contractive GARCH-type processes

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  12 July 2019

Paul Doukhan  and
Michael H. Neumann
Paul Doukhan*
Affiliation:
Université Cergy-Pontoise
Michael H. Neumann*
Affiliation:
Friedrich-Schiller-Universität Jena
*
*Postal address: UMR 8088 Analyse, Géométrie et Modélisation, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France.
**Postal address: Friedrich-Schiller-Universität Jena, Institut für Mathematik, Ernst-Abbe-Platz 2, 07743 Jena, Germany. Email address: michael.neumann@uni-jena.de
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Abstract

We prove existence and uniqueness of a stationary distribution and absolute regularity for nonlinear GARCH and INGARCH models of order (p, q). In contrast to previous work we impose, besides a geometric drift condition, only a semi-contractive condition which allows us to include models which would be ruled out by a fully contractive condition. This results in a subgeometric rather than the more usual geometric decay rate of the mixing coefficients. The proofs are heavily based on a coupling of two versions of the processes.

Keywords

Absolute regularitycouplingGARCHINGARCHmixing

MSC classification

Primary: 60G10: Stationary processes
Secondary: 60J05: Discrete-time Markov processes on general state spaces

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 1 , March 2019 , pp. 91 - 115
Copyright
© Applied Probability Trust 2019 

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