A functional wavelet-kernel approach for time series prediction

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

Volumn 68, Issue 5, 2006, Pages 837-857

  Antoniadis, Anestis ^a   Paparoditis, Efstathios ^b   Sapatinas, Theofanis ^b  

^a UNIV GRENOBLE ALPES   (France)

^b UNIVERSITY OF CYPRUS   (Cyprus)

Author keywords

mixing; Besov spaces; Exponential smoothing; Functional kernel regression; Pointwise prediction intervals; Resampling; Seasonal autoregressive integrated moving average models; Smoothing splines; Time series prediction; Wavelets

Indexed keywords

EID: 33750321905     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2006.00569.x     Document Type: Article

References (23)

1. Antoniadis, A. and Sapatinas, T. (2003) Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes. J. Multiv. Anal., 87, 133-158.
2. Besse, P. C. and Cardot, H. (1996) Approximation spline de la prévision d'un processus fonctionnel autorégressif d'ordre 1. Can. J. Statist., 24, 467-487.
3. Besse, P. C., Cardot, H. and Stephenson, D. B. (2000) Autoregressive forecasting of some functional climatic variations. Scand. J. Statist., 27, 673-687.
4. Bosq, D. (1991) Modelization, nonparametric estimation and prediction for continuous time processes. In Non-parametric Functional Estimation and Related Topics (ed. G. Roussas), pp. 509-529. Dordrecht: Kluwer.
5. Bosq, D. (1998) Nonparametric statistics for stochastic processes. Lect. Notes Statist., 110.
6. Bosq, D. (2000) Linear processes in function spaces. Lect. Notes Statist., 149.
7. Bosq, D. and Delecroix, M. (1985) Nonparametric prediction of a Hilbert-space valued random variable. Stochast. Processes Appl., 19, 271-280.
8. Box, G. E. and Jenkins, G. M. (1976) Time Series Analysis and Control. San Francisco: Holden-Day.
9. Brockwell, P. J. and Davis, R. A. (1991) Time Series: Theory and Methods, 2nd edn. New York: Springer.
10. Chatfield, C. (1980) The Analysis of Time Series, 4th edn. London: Chapman and Hall.
11. Cheng, B. and Tong, H. (1998) k-stationarity and wavelets. J. Statist. Planng Inf., 68, 129-144.
12. Daubechies, I. (1992) Ten Lectures on Wavelets. Philadelphia: Society for Industrial and Applied Mathematics.
13. Doukhan, P. (1994) Mixing: Properties and Examples. New York: Springer.
14. Ferraty, F., Goia, A. and Vieu, P. (2002) Functional nonparametric model for time series: a fractal approach for dimension reduction. Test, 11, 317-344.
15. Härdle, W. and Vieu, P. (1992) Kernel regression smoothing of time series. J. Time Ser. Anal., 13, 209-232.
16. Hart, J. D. (1996) Some automated methods of smoothing time-dependent data. J. Nonparam. Statist., 6, 115-142.
17. Lipster, R. S. and Shiryayev, A. N. (1977) Statistics of Random Processes, vol. I, General Theory. New York: Springer.
18. Mack, Y. P. and Silverman, B. W. (1982) Weak and strong uniform consistency of kernel regression estimates. Z. Wahrsch. Ver. Geb., 62, 405-415.
19. Mallat, S. G. (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattn Anal. Mach. Intell., 11, 674-693.
20. Meyer, Y. (1992) Wavelets and Operators. Cambridge: Cambridge University Press.
21. Misiti, M., Misiti, Y., Oppenheim, G. and Poggi, J.-M. (1994) Décomposition en ondelettes et méthodes comparatives: étude d'une courbe de charge électrique. Rev. Statist. Appl., 42, 57-77.
22. Pumo, B. (1998) Prediction of continuous time processes by C[0, 1]-valued autoregressive processes. Statist. Inf. Stochast. Processes, 3, 297-309.
23. Rosenblatt, M. (1956) A central limit theorem and a strong mixing condition. Proc. Natn. Acad. Sci. USA, 42, 43-47.