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 language | English |
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Pages (from-to) | 2527-2537 |
Number of pages | 11 |
Journal | Communications in Statistics - Theory and Methods |
Volume | 28 |
Issue number | 11 |
DOIs | |
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