On a mixture autoregressive model

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 62, Issue 1, 2000, Pages 95-115

  Wong, Chun Shan ^a   Li, Wai Keung ^a  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Autocorrelation; EM algorithm; Mixture autoregressive model; Model selection; Stationarity

Indexed keywords

EID: 0034358434     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00222     Document Type: Article

References (32)

1. Akaike, H. (1973) Information theory and an extension of the maximum likelihood principle. In Proc. 2nd Int. Symp. Information Theory (eds B. N. Petrov and F. Csàki), pp. 267-281. Budapest: Akademiài Kiado.
2. Beněs, V. E. (1967) Existence of finite invariant measures for Markov processes. Proc. Am. Math. Soc., 18, 1058-1061.
3. Bollerslev, T. (1986) Generalized autoregressive conditional heteroskedasticity. J. Econometr., 31, 307-327.
4. Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. (1994) Time Series Analysis: Forecasting and Control, 3rd edn. Englewood Cliffs: Prentice Hall.
5. Chan, K. S. and Tong, H. (1998) A note on testing for multi-modality with dependent data. Unpublished.
6. Chen, J. and Cheng, P. (1997) On testing the number of components in finite mixture models with known relevant component distributions. Can. J. Statist., 25, 389-400.
7. Dacunha-Castelle, D. and Gassiat, E. (1997) The estimation of the order of a mixture model. Bernoulli, 3, 279-299.
8. Davies, R. B. (1977) Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika, 64, 247-254.
9. -(1987) Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika, 74, 33-43.
10. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977) Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. R. Statist. Soc. B, 39, 1-38.
11. Elton, C. and Nicholson, M. (1942) The ten-year cycle in numbers of the lynx in Canada. J. Anim. Ecol., 11, 215-244.
12. Engle, R. F. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987-1007.
13. Engle, R. F. and Granger, C. W. J. (1987) Co-integration and error correction: representation, estimation, and testing. Econometrica, 55, 251-276.
14. Feng, Z. D. and McCulloch, C. E. (1996) Using bootstrap likelihood ratios in finite mixture models. J. R. Statist. Soc. B, 58, 609-617.
15. Gaver, D. P. and Lewis, P. A. W. (1980) First-order autoregressive Gamma sequences and point process. Adv. Appl. Probab., 12, 727-745.
16. Granger, C. W. J. and Teräsvirta, T. (1993) Modelling Nonlinear Economic Relationships, ch. 8, pp. 130-135. New York: Oxford University Press.
17. Jalali, A. and Pemberton, J. (1995) Mixture models for time series. J. Appl. Probab., 32, 123-138.
18. Lawrance, A. J. and Lewis, P. A. W. (1985) Modelling and residual analysis of nonlinear autoregressive time series in exponential variables. J. R. Statist. Soc. B, 47, 165-202.
19. 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. Am. Statist. Ass., 91, 1504-1514.
20. Louis, T. A. (1982) Finding the observed information matrix when using the EM algorithm. J. R. Statist. Soc. B, 44, 226-233.
21. Martin, R. D. and Yohai, V. J. (1985) Robustness in time series and estimating ARMA models. In Handbook of Statistics (eds E. J. Hannan, P. R. Krishnaiah and M. M. Rao), vol. 5, pp. 119-155. New York: Elsevier.
22. -(1986) Influence functionals for time series. Ann. Statist., 14, 781-855.
23. Martin, V. L. (1992) Threshold time series models as multimodal distribution jump processes. J. Time Ser. Anal., 13, 79-94.
24. Meng, X. L. and Rubin, D. B. (1991) Using EM to obtain asymptotic variance-covariance matrices: the SEM algorithm. J. Am. Statist. Ass., 86, 899-909.
25. -(1993) Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika, 80, 267-278.
26. Moran, P. A. P. (1953) The statistical analysis of the Canadian lynx cycle: I, Structure and prediction. Aust. J. Zool., 1, 163-173.
27. Richardson, S. and Green, P. J. (1997) On Bayesian analysis of mixtures with an unknown number of components (with discussion). J. R. Statist. Soc. B, 59, 731-792.
28. Schwarz, G. (1978) Estimating the dimension of a model. Ann. Statist., 6, 461-464.
29. Tanner, M. A. (1993) Tools for Statistical Inference. New York: Springer.
30. Tong, H. (1990) Non-linear Time Series. New York: Oxford University Press.
31. Wichern, D. W., Miller, R. B. and Hsu, D. (1976) Changes of variance in first-order autoregressive time series models - with an application. Appl. Statist., 25, 248-256.
32. Wong, C. S. (1998) Statistical inference for some nonlinear time series models. PhD Thesis. University of Hong Kong, Hong Kong.