Semiparametric regression smoothing of non-linear time series

Scandinavian Journal of Statistics

Volumn 25, Issue 3, 1998, Pages 521-539

  Gao, Jiti ^a  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Non linear time series; Partly linear additive autoregressive model; Semiparametric regression smoothing; mixing

Indexed keywords

EID: 0000126160     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9469.00118     Document Type: Article

References (39)

1. Auestad, B. & Tjøstheim, D. (1990). Identification of nonlinear time series: first order characterization and order determination. Biometrika 77, 669-687.
2. Boente, G. & Fraiman, R. (1988). Consistency of a nonparametric estimate of a density function for dependent variables. J. Multivariate Anal. 25, 90-99.
3. Box, G. E. & Jenkins, G. M. (1976). lem Time series analysis, forecasting and control, 2nd edn, Holden-Day, San Francisco.
4. Brockwell, P. & Davis, R. (1990). Time series theory and methods, 2nd edn. Springer, New York.
5. Chambers, J. M. & Hastie, T. J. (1992). Statistical models in S. Wadsworth and Brooks/Cole Advanced Books and Software, Pacific Grove, California.
6. Chen, R. & Tsay, R. (1993). Nonlinear additive ARX models. J. Amer. Statist. Assoc. 88, 955-967.
7. Cheng, B. & Tong, H. (1992). On consistent nonparametric order determination and chaos. J. Roy. Statist. Soc. Ser. B 54, 427-449.
8. Cheng, B. & Tong, H. (1993). Nonparametric function estimation in noisy chaos. Developments in time series analysis (In honour of Maurice B. Priestley, ed. T. Subba Rao). Chapman & Hall, London.
9. Craven, P. & Wahba, G. (1979). Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation. Numer. Math. 31, 377-403.
10. DeVore, R. A. & Lorentz, G. G. (1993). Constructive approximation. Springer, New York.
11. Doukhan, P. (1995). Mixing: properties and examples. Lecture Notes in Statistics 85, Springer, New York.
12. Engle, R. F., Granger, C. W., Rice, J. & Weiss, A. (1986). Semiparametric estimates of the relation between weather and electricity sales. J. Amer. Statist. Assoc. 81, 310-320.
13. Gao, J. T. (1995a). Asymptotic properties of some estimates for partly linear autoregressive models. Statist. Theory Methods 24, 2011-2026.
14. Gao, J. T. (1995b). Adaptive parametric test in a semiparametric regression model. Statist. Theory Methods 26, 783-800.
15. Gao, J. T. (1996). Semiparametric regression smoothing of nonlinear time series. Technical report, No. 9612, School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.
16. Gao, J. T. & Liang, H. (1995a). Asymptotic normality of pseudo-LS estimator for partly linear autoregressive models. Statist. Probab. Lett. 23, 27-34.
17. Gao, J. T. & Liang, H. (1995b). Statistical inference in semiparametric single-index and partially nonlinear regression models. Ann. Inst. Statist. Math. 49, 493-517.
18. Gao, J. T. & Shi, P. D. (1995). M -type smoothing splines in nonparametric and semiparametric regression models. Statist. Sinica 7, 1155-1169.
19. Gao, J. T. & Yee, T. W. (1996). Adaptive estimation in partly linear additive (semiparametric) autoregressive models. Technical report. No. 9611, School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.
20. Glass, L. & Mackey, M. (1988). From clocks to chaos: the rhythms of life. Princeton University Press. Princeton, N.J.
21. Green, P. J., Jennison, C. & Seheult, A. (1985). Analysis of field experiments by least squares smoothing. J. Roy. Statist. Soc. Ser. B 47, 299-315.
22. Györfi, L., Härdle, W., Sarda, P. & Vieu, P. (1989). Nonparametric curve estimation for time series. Lecture Notes in Statistics 60, Springer, New York.
23. Härdle, W. & Vieu, P. (1992). Kernel regression smoothing of time series. J. Time Ser. Anal. 13, 209-232.
24. Härdle, W., Hall, P. & Marron, S. (1988). How far are the optimally chosen smoothing parameters for their optimum? J. Amer. Statist. Assoc. 83, 86-95.
25. Hart, J. & Vieu, P. (1990). Data-driven bandwidth choice for density estimation based on dependent data. Ann. Statist. 18, 873-890.
26. Kashin, B. S. & Saakyan, A. A. (1989). Orthogonal series. Translations of Mathematical Monographs, Vol. 75, American Mathematical Society.
27. Nychka, D., Elliner, S., Gallant, A. & McCaffrey, D. (1992). Finding chaos in noisy systems. J. Roy. Statist. Soc. Ser. B 54, 399-426.
28. Pollard, D. (1984). Convergence of stochastic processes. Springer, New York.
29. Readshaw, J. L. & Cuff, W. R. (1980). A model of Nicholson's blowfly cycles and its relevance to predation theory. J. Anim. Ecol. 49, 1005-1010.
30. Robinson, P. M. (1988). Root-N-consistent semiparametric regression. Econometrica 56, 931-954.
31. Seber, G. A. F. (1977). Linear regression analysis. Wiley, New York.
32. Speckman, P. (1988). Kernel smoothing in partial linear models. J. Roy. Statist. Soc. Ser. B 50, 413-436.
33. Tjøstheim, D. (1990). Non-linear time series and Markov chains. Adv. Appl. Probab. 22, 587-611.
34. Tjøstheim, D. (1994). Non-linear time series: a selective review. Scand. J. Statist. 21, 97-130.
35. Tong, H. (1990). Non-linear time series. Oxford University Press, Oxford.
36. Vieu, P. (1994). Choice of regressors in nonparametric estimation. Comput. Statist. Data Anal. 17, 575-594.
37. Vieu, P. (1995). Order choice in nonlinear autoregressive models. Statistics 26, 307-328.
38. Wahba, G. (1984). Partial spline models for the semiparametric estimation of functions of several variables. In Analysis for time series, 319-329. Institute of Statistical Mathematics, Tokyo.
39. Yao, Q. W. & Tong, H. (1994). On subset selection in nonparametric stochastic regression. Statist. Sinica 4, 51-70.