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Absolute regularity of semi-contractive GARCH-type processes. (English) Zbl 1418.60029

Summary: 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.

MSC:

60G10 Stationary stochastic processes
60J05 Discrete-time Markov processes on general state spaces
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