Absolute regularity of semi-contractive GARCH-type processes. (March 2019)

• Record Type: Journal Article
• Authors: Doukhan, Paul; Neumann, Michael H.
• Is Part Of: Journal of applied probability. Volume 56:Number 1(2019)
• Page Start: 91
• Page End: 115
• Publication Date: 2019-03
• Subjects: Absolute regularity, -- coupling, -- GARCH, -- INGARCH, -- mixing; Primary 60G10, -- Secondary 60J05; 519.2
• DOI: 10.1017/jpr.2019.8
• Languages: English
• ISSNs: 0021-9002

Abstract

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.