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

Oesook Lee

doi:10.1080/03610929908832436

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

Oesook Lee

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Pages (from-to)	2527-2537
Number of pages	11
Journal	Communications in Statistics - Theory and Methods
Volume	28
Issue number	11
DOIs	https://doi.org/10.1080/03610929908832436
State	Published - 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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10.1080/03610929908832436

Cite this

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

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\}.",

keywords = "Ergodicity, Geometric ergodicity, Markov chain",

author = "Oesook Lee",

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.",

year = "1999",

doi = "10.1080/03610929908832436",

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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 - https://www.scopus.com/pages/publications/28244480419

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 -

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

Abstract

Bibliographical note

Keywords

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Cite this