Geometric transience of nonlinear time series

Statistica Sinica

Volumn 11, Issue 1, 2001, Pages 273-287

  Cline, Daren B H ^a   Pu, Huay Min H ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Markov chain; Nonlinear time series; Transience

Indexed keywords

EID: 0035592177     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. An, H. Z. and Huang, F. C. (1996). The geometrical ergodicity of nonlinear autoregressive models. Statist. Sinica 6, 943-956.
2. Bhattacharya, R. and Lee, C. (1995). Ergodicity of nonlinear first order autoregressive models. J. Theory Probab. 8, 207-219.
3. Chan, K.-S. (1990). Deterministic stability, stochastic stability, and ergodicity. Appendix 1 in Non-linear Time Series Analysis: A Dynamical System Approach (by H. Tong). Oxford University Press, London.
4. Chan, K.-S. and Tong, H. (1985). On the use of the deterministic Lyapunov function for the ergodicity of stochastic difference equations. Adv. Appl. Probab. 17, 666-678.
5. Chan, K.-S. and Tong, H. (1986). On estimating thresholds in autoregressive models. J. Time Ser. Anal. 7, 179-190.
6. Chan, K.-S. and Tong, H. (1994). A note on noisy chaos. J. Roy. Statist. Soc. Ser. B 56, 301-311.
7. Chan, K.-S., Petruccelli, J. D., Tong, H. and Woolford, S. W. (1985). A multiple threshold AR(1) model. J. Appl. Probab. 22, 267-279.
8. Chen, R. and Tsay, R. S. (1993a). Functional-coefficient autoregressive models. J. Amer. Statist. Assoc. 88, 298-308.
9. Chen, R. and Tsay, R. S. (1993b). Nonlinear Additive ARX models. J. Amer. Statist. Assoc. 88, 955-967.
10. Cline, D. B. H. and Pu, H. H. (1998). Verifying irreducibility and continuity of a nonlinear time series. Statist. Probab. Lett. 40, 139-148.
11. Cline, D. B. H. and Pu, H. H. (1999a). Geometric ergodicity of nonlinear time series. Statist. Sinica 9, 1103-1118.
12. Cline, D. B. H. and Pu, H. H. (1999b). Stability of nonlinear AR(1) time series with delay. Stoch. Proc. Appl. 82, 307-333.
13. Cline, D. B. H. and Pu, H. H. (1999c). Stability of threshold-like ARMA time series. Statistics Department., Texas A&M University.
14. Gradshteyn, I. S. and Ryzhik, I. M. (1980). Table of Integrals, Series and Products. Academic Press, Orlando, FL.
15. Guo, M. and Petruccelli, J. D. (1991). On the null recurrence and transience of a first-order SETAR model. J. Appl. Probab. 28, 584-592.
16. Kendall, D. G. (1959). Unitary dilations of Markov transition operators and the corresponding integral representations for transition-probability matrices. In Probab. Statist. (Edited by U. Granander), 139-161. Almqvist and Wiksell, New York.
17. Kingman, J. F. C. (1963). The exponential decay of Markov transition probabilities. Proc. London Math. Soc. 13, 337-358.
18. Lu, Z. (1998a). Geometric ergodicity of a general ARCH type model with applications to some typical models. In Adv. Operations Research Systems Engineering (Edited by J. Gu, G. Fan and S. Wang), 76-86. Global-Link Informatics Ltd.
19. Lu, Z. (1998b). On the geometric ergodicity of a non-linear autoregressive model with an autoregressive conditional heteroscedastic term. Statist. Sinica 8, 1205-1217.
20. Meyn, S. P. and Tweedie, R. L. (1993). Markov Chains and Stochastic Stability. Springer-Verlag, London.
21. Petruccelli, J. D. and Woolford, S. W. (1984). A threshold AR(1) model. J. Appl. Probab. 21, 587-611.
22. Pham D. T. (1985). Bilinear Markovian representation and bilinear models. Stoch. Proc. Appl. 20, 295-306.
23. Rao, C. R. (1973). Linear Statistical Inference and Its Applications. 2nd edition. Wiley, New York.
24. Tjøstheim, D. (1990). Non-linear time series and Markov chains. Adv. Appl. Probab. 22, 587-611.
25. Tjøstheim, D. and Auestad, B. H. (1994a). Nonparametric identification of nonlinear time series: projections. J. Amer. Statist. Assoc. 89, 1398-1409.
26. Tjøstheim, D. and Auestad, B. H. (1994b). Nonparametric identification of nonlinear time series: selecting significant lags. J. Amer. Statist. Assoc. 89, 1410-1419.
27. Vere-Jones, D. (1962). Geometric ergodicity in denumerable Markov chains. Quart. J. Math. Oxford 13, 7-28.