TY - JOUR

T1 - Strict stationarity of AR(P) processes generated by nonlinear random functions with additive perturbations

AU - Lee, Oesook

N1 - 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.

PY - 1999

Y1 - 1999

N2 - 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}.

AB - 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}.

KW - Ergodicity

KW - Geometric ergodicity

KW - Markov chain

UR - http://www.scopus.com/inward/record.url?scp=28244480419&partnerID=8YFLogxK

U2 - 10.1080/03610929908832436

DO - 10.1080/03610929908832436

M3 - Article

AN - SCOPUS:28244480419

SN - 0361-0926

VL - 28

SP - 2527

EP - 2537

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 11

ER -