The tail of the stationary distribution of an autoregressive process with ARCH(1) errors

Milan Borkovec, Claudia Klüppelberg

Publikation: Beitrag in FachzeitschriftArtikelBegutachtung

74 Zitate (Scopus)

Abstract

We consider the class of autoregressive processes with ARCH(1) errors given by the stochastic difference equation Xn = αXn-1 + √ β + λX2n-1εn, n ∈ ℕ, where (εn)n∈ℕ i.i.d. random variables. Under general and tractable assumptions we show the existence and uniqueness of a stationary distribution. We prove that the stationary distribution has a Pareto-like tail with a well-specified tail index which depends on α, λ and the distribution of the innovations (εn)n∈ℕ. This paper generalizes results for the ARCH(1) process (the case α = 0). The generalization requires a new method of proof and we invoke a Tauberian theorem.

OriginalspracheEnglisch
Seiten (von - bis)1220-1241
Seitenumfang22
FachzeitschriftAnnals of Applied Probability
Jahrgang11
Ausgabenummer4
DOIs
PublikationsstatusVeröffentlicht - Nov. 2001

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