The ARHD model

Journal of Statistical Planning and Inference

Volumn 137, Issue 2, 2007, Pages 538-553

  Mas, André ^a   Pumo, Besnik ^b  

^a UNIV MONTPELLIER   (France)

^b INH Angers   (France)

Author keywords

ARHD model; Continuous time prediction; ENSO; Functional data; Sobolev space; Wong process

Indexed keywords

EID: 33749502424     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2005.12.006     Document Type: Article

References (28)

1. Adams R.A., and Fournier J.J.F. Sobolev Spaces. second ed (2003), Academic Press, New York
2. Antoniadis A., and Sapatinas T. Wavelet methods for continuous-time prediction using representations of autoregressive processes in Hilbert spaces. J. Multivariate Anal. 87 (2003) 133-158
3. Besse P., and Cardot H. Approximation spline de la prévision d'un processus fonctionnel autorégressif d'ordre 1. Canad. J. Statist. 24 (1996) 467-487
4. Besse P., Cardot H., and Stephenson D. Autoregressive forecasting of some climatic variations. Scand. J. Statist. 27 (2000) 673-687
5. Blanke D., and Pumo B. Optimal sampling for density estimation in continuous time. J. Time Ser. Anal. 24 1 (2003) 1-23
6. Bosq, D., 1991. Modelization, nonparametric estimation and prediction for continuous time processes. In: Roussas (Ed.), Nato Asi Series C, vol. 335, pp. 509-529.
7. Bosq, D., 2000. Linear Processes in Function Spaces. Lectures Notes in Statistics. Springer, Berlin.
8. Brockwell P., and Davis A. Time Series: Theory and Methods (1987), Springer, Berlin
9. Cardot H., Ferraty F., and Sarda P. Functional linear model. Statist. Probab. Lett. 45 (1999) 11-22
10. Dunford, N., Schwartz, J.T., 1988. Linear Operators, vols. I, II. Wiley Classics Library, New York.
11. Ferraty F., and Vieu P. The functional nonparametric model and application to spectrometric data. Comput. Statist. 17 4 (2003) 545-564
12. Gohberg, I., Goldberg, S., Kaashoek, M.A., 1991. Classes of Linear Operators. Operator Theory: Advances and Applications, vols. I, II. Birkhaüser, Basel.
13. Grenander U. Abstract Inference (1981), Wiley, New York
14. Hoel P.G., Port S.C., and Stone C.J. Introduction to Stochastic Processes (1972), Waveland Press, Inc
15. Ledoux M., and Talagrand M. Probability in Banach Spaces-Isoperimetry and Processes (1991), Springer, Berlin
16. Marion J.M., and Pumo B. Comparaison des modèles ARH(1) et ARHD(1) sur des données physiologiques. Ann. l'ISUP 48 3 (2004) 29-38
17. Mas A. Normalité asymptotique de l'estimateur empirique de l'opérateur d'autocorrélation d'un processus ARH(1). C. R. Acad. Sci. Sér. I t.329 (1999) 899-902
18. Mas A., and Menneteau L. Perturbation approach applied to the asymptotic study of random operators. Progr. Probab. 55 (2003) 127-134
19. Mas A., and Menneteau L. Large and moderate deviations for infinite-dimensional autoregressive processes. J. Multivariate Anal. 87 (2003) 241-260
20. Mourid, T., 1995. Contribution à la statistique des processus autorégressifs à temps continu. Ph.D. Thesis, University of Paris VI.
21. Pumo, B., 1992. Estimation et prévision de processus autorégressifs fonctionnels. Applications aux processus à temps continu. Ph.D. Thesis, University of Paris VI.
22. Pumo B. Prediction of continuous time processes by C [0, 1]-valued autoregressive process. Statist. Inference Stoch. Process. 1 3 (1998) 297-309
23. Ramsay J.O., and Silverman B.W. Functional Data Analysis (1997), Springer, Berlin
24. Silverman B.W. Smoothed functional principal component analysis by choice of norm. Ann. Statist. 24 1 (1996) 1-24
25. Smith T.M., Reynolds R.W., Livezey R.E., and Stokes D.C. Reconstruction of historical sea surface temperatures using empirical orthogonal functions. J. Climate 9 6 (1996) 1403-1420
26. Tikhonov A.N., and Arsenin V.Y. Solutions of Ill-posed Problems (1977), V.H. Winstons and Sons, Washington, DC
27. Wong E. Some results concerning the zero-crossings of Gaussian noise. SIAM J. Appl. Math. 14 6 (1966) 1246-1254
28. Ziemer, W.P., 1989. Weakly Differentiable Functions. Sobolev Spaces and Functions of Bounded Variations. Graduate Text in Mathematics, vol. 120. Springer, New York.