Semiparametric non-linear time series model selection

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

Volumn 66, Issue 2, 2004, Pages 321-336

  Gao, Jiti ^a   Tong, Howell ^b,c  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

^c LONDON SCHOOL OF ECONOMICS   (United Kingdom)

Author keywords

Linear model; Mixing process; Model selection; Non linear time series; Nonparametric regression; Semiparametric regression; Strictly stationary process; Variable selection

Indexed keywords

EID: 2442501365     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1369-7412.2004.05303.x     Document Type: Article

References (37)

1. Bickel, P. and Zhang, P. (1992) Variable selection in nonparametric regression with categorical covariates. J. Am. Statist. Ass., 87, 90-97.
2. Chen, R., Liu, J. and Tsay, R. (1995) Additivity tests for nonlinear autoregression. Biometrika, 82, 369-383.
3. Chen, R. and Tsay, R. (1993) Nonlinear additive ARX models. J. Am. Statist. Ass., 88, 955-967.
4. Cheng, B. and Tong, H. (1992) On consistent nonparametric order determination and chaos. J. R. Statist. Soc. B, 54, 427-449.
5. Cheng, B. and Tong, H. (1993) Nonparametric function estimation in noisy chaos. In Developments in Time Series Analysis (ed. T. Subba Rao), pp. 183-206. London: Chapman and Hall.
6. Fan, J. and Gijbels, I. (1996) Local Polynomial Modelling and Its Applications. London: Chapman and Hall.
7. Gao, J. (1998) Semiparametric regression modelling of nonlinear time series. Scand. J. Statist., 25, 521-539.
8. Gao, J. and Liang, H. (1995) Asymptotic normality of pseudo-LS estimator for partially linear autoregressive models. Statist. Probab. Lett., 23, 27-34.
9. Gao, J. and Tong, H. (2002) Model selection in semiparametric time series regression. Working Paper. School of Mathematics and Statistics, University of Western Australia, Crawley. (Available from http://www.maths. uwa.edu.au/~jiti/kao45.pdf.)
10. Gao, J., Tong, H. and Wolff, R. C. L. (2002a) Adaptive series estimation in additive stochastic regression models. Statist. Sin., 12, 409-428.
11. Gao, J., Tong, H. and Wolff, R. C. L. (2002b) Model specification tests in nonparametric stochastic regression models. J. Multiv. Anal., 83, 324-359.
12. Gao, J. and Yee, T. (2000) Adaptive estimation in partially linear (semiparametric) autoregressive models. Can. J. Statist., 28, 571-586.
13. Härdle, W., Liang, H. and Gao, J. (2000) Partially Linear Models. New York: Springer.
14. Härdle, W., Lütkepohl, H. and Chen, R. (1997) A review of nonparametric time series analysis. Int. Statist. Rev., 65, 49-72.
15. Masry, E. (1996) Multivariate regression estimation-local polynomial fitting for time series. Stoch. Processes Appl., 65, 81-101.
16. Masry, E. and Tjøstheim, D. (1995) Nonparametric estimation and identification of nonlinear ARCH time series. Econometr. Theory, 11, 258-289.
17. Masry, E. and Tjøstheim, D. (1997) Additive nonlinear ARX time series and projection estimates. Econometr. Theory, 13, 214-252.
18. Shao, J. (1993) Linear model selection by cross-validation. J. Am. Statist. Ass., 88, 486-494.
19. Shao, J. (1997) An asymptotic theory for linear model selection (with comments). Statist. Sin., 7, 221-264.
20. Shi, P. and Tsai, C. L. (1999) Semiparametric regression model selections. J. Statist. Planng Inf., 77, 119-139.
21. Stone, M. (1977) An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion. J. R. Statist. Soc. B, 39, 44-47.
22. Teräsvirta, T., Tjøstheim, D. and Granger, C. W. J. (1994) Aspects of modelling nonlinear time series. In Handbook of Econometrics (eds R. F. Engle and D. L. McFadden), vol. 4, pp. 2919-2957.
23. Tjøstheim, D. (1994) Nonlinear time series: a selective review. Scand. J. Statist., 21, 97-130.
24. Tjøstheim, D. (1999) Nonparametric specification procedures for time series. In Asymptotics, Nonparametrics, and Time Series, vol. 158, pp. 149-199. New York: Dekker.
25. Tjøstheim, D. and Auestad, B. (1994a) Nonparametric identification of nonlinear time series: projections. J. Am. Statist. Ass., 89, 1398-1409.
26. Tjøstheim, D. and Auestad, B. (1994b) Nonparametric identification of nonlinear time series: selecting significant lags. J. Am. Statist. Ass., 89, 1410-1419.
27. Tong, H. (1976) Fitting a smooth moving average to noisy data. IEEE Trans. Inform. Theory, 26, 493-496.
28. Tong, H. (1990) Nonlinear Time Series. Oxford: Oxford University Press.
29. Tschernig, R. and Yang, L. (2000) Nonparametric lag selection for time series. J. Time Ser. Anal., 21, 457-487.
30. Vieu, P. (1994) Choice of regressors in nonparametric estimation. Comput. Statist. Data Anal., 17, 575-594.
31. Vieu, P. (1995) Order choice in nonlinear autoregressive models. Statistics, 26, 307-328.
32. Vieu, P. (2002) Data-driven model choice in multivariate nonparametric regression. Statistics, 36, 231-245.
33. Xia, Y., Tong, H., Li, W. K. and Zhu, L.-X. (2002) An adaptive estimation of dimension reduction space (with discussion). J. R. Statist. Soc. B, 64, 363-410.
34. Yang, Y. (1999) Model selection for nonparametric regression. Statist. Sin., 9, 475-500.
35. Yao, Q. and Tong, H. (1994) On subset selection in nonparametric stochastic regression. Statist. Sin., 4, 51-70.
36. Zhang, P. (1991) Variable selection in nonparametric regression with continuous covariates. Ann. Statist., 19, 1869-1882.
37. Zhang, P. (1993) Model selection via multifold cross-validation. Ann. Statist., 21, 299-313.