Journal article
A multiple-threshold AR(1) model
Journal of applied probability, Vol.22(2), pp.267-279
06/1985
DOI: 10.2307/3213771
Abstract
We consider the model Zt = φ (0, k)+ φ(1, k)Zt–1 + at (k) whenever rk−1<Zt−1≦rk, 1≦k≦l, with r0 = –∞ and rl =∞. Here {φ (i, k); i = 0, 1; 1≦k≦l} is a sequence of real constants, not necessarily equal, and, for 1≦k≦l, {at(k), t≧1} is a sequence of i.i.d. random variables with mean 0 and with {at(k), t≧1} independent of {at(j), t≧1} for j ≠ k. Necessary and sufficient conditions on the constants {φ (i, k)} are given for the stationarity of the process. Least squares estimators of the model parameters are derived and, under mild regularity conditions, are shown to be strongly consistent and asymptotically normal.
Details
- Title: Subtitle
- A multiple-threshold AR(1) model
- Creators
- K. S. ChanJoseph D. PetruccelliH. TongSamuel W. Woolford
- Resource Type
- Journal article
- Publication Details
- Journal of applied probability, Vol.22(2), pp.267-279
- DOI
- 10.2307/3213771
- ISSN
- 0021-9002
- eISSN
- 1475-6072
- Language
- English
- Date published
- 06/1985
- Academic Unit
- Statistics and Actuarial Science; Radiology
- Record Identifier
- 9984257609402771
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