Geometric ergodicity of nonlinear time series

Statistica Sinica

Volumn 9, Issue 4, 1999, Pages 1103-1118

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

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Ergodicity; Markov chain; Nonlinear time series

Indexed keywords

EID: 0033262354     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (35)

1. An, H. Z. and Huang, F. C. (1996). The geometrical ergodicity of nonlinear autoregressive models. Statist. Sinica 6, 943-956.
2. Brockwell, P. J., Liu, J. and Tweedie, R. L. (1992). On the existence of stationary threshold autoregressive moving-average processes. J. Time Series Anal. 13, 95-107.
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. (1993). A review of some limit theorems of Markov chains and their applications. Dimensions, Estimation and Models (Edited by H. Tong), 108-135. World Scientific, Singapore.
5. Chan, K. S., Petrucelli, J. D., Tong, H. and Woolford, S. W. (1985). A multiple threshold AR(1) model. J. Appl. Probab. 22, 267-279.
6. 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.
7. Chan, K. S. and Tong, H. (1986). On estimating thresholds in autoregressive models. J. Time Ser. Anal. 7, 179-190.
8. Chan, K. S. and Tong, H. (1994). A note on noisy chaos. J. Roy. Statist. Soc. 56, 301-311.
9. Chen, R. and Tsay, R. S. (1991). On the ergodicity of TAR(1) process. Ann. Appl. Probab. 1, 613-634.
10. Chen, R. and Tsay, R. S. (1993a). Functional-coefficient autogressive models. J. Amer. Statist. Assoc. 88, 298-308.
11. Chen, R. and Tsay, R. S. (1993b). Nonlinear additive ARX models. J. Amer. Statist. Assoc. 88, 955-967.
12. Cline, D. B. H. and Pu, H. H. (1998a). Geometric transience of nonlinear time series. Technical Report 289, Dept. of Statistics, Texas A&M University, College Station, TX.
13. Cline, D. B. H. and Pu, H. H. (1998b). Verifying irreducibility and continuity of a nonlinear time series. Statist. Probab. Lett. 40, 139-148.
14. Cline, D. B. H. and Pu, H. H. (1999). Stability of nonlinear AR(1) time series with delay. Stoch. Proc. Appl. 82, 307-333.
15. Foster, F. G. (1953). On the stochastic matrices associated with certain queueing processes. Ann. Math. Stat. 24, 355-360.
16. Gradshteyn, I. S. and Ryzhik, I. M. (1980). Table of Integrals, Series and Products. Academic Press, Orlando, FL.
17. Guégan, D. and Diebolt, J. (1994). Probabilistic properties of the β-ARCH model. Statist. Sinica 4, 71-87.
18. Guo, M. and Petrucelli, J. D. (1991). On the null-recurrence and transience of a first order SETAR model. J. Appl. Probab. 28, 584-592.
19. Härdle, W., Lütkepohl, H. and Chen, R. (1997). A review of nonparametric time series analysis. Intern'l. Stat. Review 65, 49-72.
20. Jones, D. A. (1978). Nonlinear autoregressive processes. Proc. Roy. Soc. A360, 71-95.
21. Lim, K. S. (1992). On the stability of a threshold AR(1) without intercepts. J. Time Ser. Anal. 13, 119-132.
22. Lu, Z. (1996). Geometric ergodicity of a vector non-linear AR model mixed with an ARCH term. Preprint, Inst. Stat., Univ. Catholique de Louvain, Leuven, Belgium.
23. Meyn, S. P. and Tweedie, R. L. (1992). Stability of Markovian processes I: criteria for discrete-time chains. Adv. Appl. Probab. 24, 542-574.
24. Meyn, S. P. and Tweedie, R. L. (1993). Markov Chains and Stochastic Stability. Springer-Verlag, London.
25. Nummelin, E. (1984). General Irreducible Markov Chains and Non-negative Operators. Cambridge University Press, Cambridge.
26. Ozaki, T. and Oda, H. (1978). Non-linear time series model identification by Akaike's information criterion. Proc. IFAC Workshop on Information and Systems, Compeign, France, October 1977.
27. Petrucelli, J. D. and Woolford, S. W. (1984). A threshold AR(1) model. J. Appl. Probab. 21, 270-286.
28. Pu, H. H. (1995). Recurrence and transience for autoregressive nonlinear time series. Dissertation, Texas A&M University, College Station, TX.
29. Spieksma, F. M. and Tweedie, R. L. (1994). Strengthening ergodicity to geometric ergodicity for Markov chains. Stochastic Models 10, 45-74.
30. Tjøstheim, D. (1990). Non-linear time series and Markov chains. Adv. Appl. Probab. 22, 587-611.
31. Tjøstheim, D. and Auestad, B. H. (1994a). Nonparametric identification of nonlinear time series: projections. J. Amer. Stat. Assoc. 89, 1398-1409.
32. Tjøstheim, D. and Auestad, B. H. (1994b). Nonparametric identification of nonlinear time series: selecting significant lags. J. Amer. Stat. Assoc. 89, 1410-1419.
33. Tong, H. (1990). Non-linear Time Series Analysis: A Dynamical System Approach. Oxford University Press, London.
34. Tweedie, R. L. (1975). Sufficient conditions for ergodicity and recurrence of Markov chains on a general state space. Stoch. Proc. Appl. 3, 385-403.
35. Tweedie, R. L. (1976). Criteria for classifying general Markov chains. Adv. Appl. Probab. 24, 542-574.