On probabilistic properties of nonlinear ARMA(p,q) models

Oesook Lee

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We consider a general nonlinear ARMA(p,q) model Xn+1=h(en-q+1,...,en,X n-p+1,...,Xn)+en+1, where h:Rp+q→R is a measurable function and {en:n≥1} is an i.i.d. sequence of random variables. Sufficient conditions for stationarity and geometric ergodicity of {Xn} are obtained by considering the asymptotic behaviours of the associated Markov chain.

Original languageEnglish
Pages (from-to)121-131
Number of pages11
JournalStatistics and Probability Letters
Issue number2
StatePublished - 15 Jan 2000

Bibliographical note

Funding Information:
This research is supported by the grants form Korea Ministry of Science and Engineering, 1997.


  • 60F05
  • 60J05
  • Ergodicity
  • Geometric ergodicity
  • Markov chain
  • Nonlinear ARMA (p,q) model
  • Stationarity


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