Stability of mixtures of vector autoregressions with autoregressive conditional heteroskedasticity

Statistica Sinica

Volumn 17, Issue 1, 2007, Pages 221-239

  Saikkonen, Pentti ^a  

^a UNIVERSITY OF HELSINKI   (Finland)

Author keywords

mixing; Autoregressive conditional heteroskedasticity; Geometric ergodicity; Markov chain; Mixture autoregressive model; Nonlinear vector autoregressive model; Stability

Indexed keywords

EID: 34248579238     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. Brockwell, P. J. and Davis, R. A. (1991). Time Series: Theory and Methods. Springer-Verlag, New York.
2. Battacharya, R. N. and Lee, C. (1995). Ergodicity of nonlinear first order autoregressive models. J. Theoret. Probab. 8, 207-219.
3. Chan, K. S. (1990). Deterministic stability, stochastic stability, and ergodicity. Appendix 1 of H. Tong (1990). Non-linear Time Series: A Dynamical System Approach, Clarendon Press, Oxford.
4. Chan, K. S., Petrucelli, J., Tong, H. and Woolford, S. W. (1985). A multiple threshold AR(1) model. J. Appl Probab. 22, 267-279.
5. 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.
6. Chan, K. S. and Tong, H. (1986). On estimating thresholds in autoregressive models. J. Time Ser. Anal. 7, 179-190.
7. Chen, M. and Chen, G. (2000). Geometric ergodicity of nonlinear autoregressive models with changing conditional variances. Canad. J. Statist. 28, 605-613.
8. Chen, G. and Chen, M. (2001). On a class of nonlinear AR(p) models with nonlinear ARCH errors. Austral. N. Z. J. Statist. 43, 445-454.
9. Cline, D. B. H. and Pu, H. H. (1998). Verifying irreducibility and continuity of a nonlinear time series. Statist. Probab. Lett. 40, 139-148.
10. Cline, D. B. H. and Pu, H. H. (1999). Geometric ergodicity of nonlinear time series. Statist. Sinica 9, 1103-1118.
11. Doukhan, P. (1994). Mixing, Properties and Examples. Springer-Verlag, New York.
12. Engle, R. F. and Kroner, K. F. (1995). Multivariate simultaneous generalized GARCH. Econom. Theory 11, 122-150.
13. Feigin, P. D. and Tweedie, R. L. (1985). Random coefficient autoregressive processes: A Markov chain analysis of stationarity and finiteness of moments. J. Time Ser. Anal. 6, 1-14.
14. Hansen, B. E. (1996). Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 64, 413-430.
15. Hansen, B. E. (2000). Sample splitting and threshold estimation. Econometrica 68, 575-603.
16. Hansen, E. and Rahbek, A. (1998). Stationarity and asymptotics of multivariate ARCH time series with an application to robustness of cointegration analysis. Preprint No. 12, 1998. Department of Statistics. University of Copenhagen.
17. Le, N. D., Martin, R. D. and Raftery, A. E. (1996). Modeling flat stretches, bursts, and outliers in time series using mixture transition distribution models. J. Amer. Statist. Assoc. 91, 1504-1515.
18. Liebscher, E. (2005). Towards a unified approach for proving geometric ergodicity and mixing properties of nonlinear autoregressive processes. J. Time Ser. Anal. 26, 669-689.
19. Ling, S. (2006). A double AR(p) model: structure and estimation. Statist Sinica, accepted.
20. Lu, Z. (1998). On the geometric ergodicity of a non-linear autoregressive model with an autoregressive conditional heteroskedastic term. Statist. Sinica 8, 1205-1217.
21. 1 geometric ergodicity of a multivariate nonlinear AR model with an ARCH term. Statist. Probab. Lett. 51, 121-130.
22. Lütkepohl, H. (1996). Handbook of Matrices. John Wiley and Sons. Chichester.
23. Luukkonen, R., Saikkonen, P. and Terasvirta, T. (1988). Testing linearity against smooth transition autoregressive models. Biometrika 75, 491-499.
24. Masry, E. and Tjøstheim, D. (1995). Nonparametric estimation and identification of nonlinear ARCH time series. Econom. Theory 11, 258-289.
25. Meyn, S. P. and Tweedie, R. L. (1993). Markov Chains and Stochastic Stability. Springer-Verlag, New York.
26. Nicholls, D. F. and Quinn, B. G. (1982). Random Coefficient Autoregressive Models: An Introduction. Springer-Verlag, New York.
27. Pham, T. D. (1985). Bilinear Markovian representation and bilinear models. Stochastic Process. Appl. 20, 295-306.
28. Pham, D. T. (1986). The mixing property of bilinear and generalised random coefficient autoregressive models. Stochastic Process. Appl. 23, 291-300.
29. Wong, C. S. and Li, W. K. (2000). On a mixture autoregressive model. J. Roy. Statist. Soc. Ser. B 62, 95-115.
30. Wong, C. S. and Li, W. K. (2001). On a mixture autoregressive conditional heteroscedastic model. J. Amer. Statist. Assoc. 96, 982-995.