Strict stationarity of AR(P) processes generated by nonlinear random functions with additive perturbations

Oesook Lee

Research output: Contribution to journalArticlepeer-review

Abstract

Let {Xn} be a generalized autoregressive process of order p defined by Xn = φn(Xn-p, ⋯ , Xn-1) + ηn, where {φn} is a sequence of i.i.d. random maps taking values on H, and {ηn} is a sequence of i.i.d. random variables. Let H be a collection of Borel measurable functions on Rp to R. By considering the associated Markov process, we obtain sufficient conditions for stationarity, (geometric) ergodicity of {Xn}.

Original languageEnglish
Pages (from-to)2527-2537
Number of pages11
JournalCommunications in Statistics - Theory and Methods
Volume28
Issue number11
DOIs
StatePublished - 1999

Bibliographical note

Funding Information:
The author would like to thank anonynlous referees for careful reading. This work was supported by a grant from Korea Ministry of Science and Technology, 1997.

Keywords

  • Ergodicity
  • Geometric ergodicity
  • Markov chain

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