A multiple-threshold AR(1) model
- 1 June 1985
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 22 (2) , 267-279
- https://doi.org/10.2307/3213771
Abstract
We consider the modelZt=φ(0,k)+ φ(1,k)Zt–1+at(k) wheneverrk−1<Zt−1≦rk, 1≦k≦l, withr0= –∞ andrl=∞. 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} forj≠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.Keywords
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