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November, 1991 On the Ergodicity of Tar(1) Processes
Rong Chen, Ruey S. Tsay
Ann. Appl. Probab. 1(4): 613-634 (November, 1991). DOI: 10.1214/aoap/1177005841


This paper establishes a necessary and sufficient condition for geometrical ergodicity for the general first-order threshold autoregressive processes. This is achieved by investigating the nonlinear dynamic behavior generated by the delay parameter of a threshold model. The ergodic region turns out to be unbounded which is different from that of a linear process.


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Rong Chen. Ruey S. Tsay. "On the Ergodicity of Tar(1) Processes." Ann. Appl. Probab. 1 (4) 613 - 634, November, 1991.


Published: November, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0795.93099
MathSciNet: MR1129777
Digital Object Identifier: 10.1214/aoap/1177005841

Primary: 93E15
Secondary: 62M99 , 93E03

Keywords: Geometrical ergodicity , nonlinear time series , threshold autoregressive model

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.1 • No. 4 • November, 1991
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