A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series

Annals of Statistics

Volumn 36, Issue 4, 2008, Pages 1925-1956

  Moulines, E ^a,c   Roueff, F ^a,c   Taqqu, M S ^b,d  

^a INSTITUT TELECOM   (France)

^b BOSTON UNIVERSITY   (United States)

^c TELECOM PARISTECH   (France)

^d Boston University   (United States)

Author keywords

Long memory; Semiparametric estimation; Wavelet analysis

Indexed keywords

EID: 51049113003     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/07-AOS527     Document Type: Article

References (23)

1. ABRY, P. and VEITCH, D. (1998). Wavelet analysis of long-range-dependent traffic. IEEE Trans. Inform. Theory 44 2-15. MR1486645
2. BOYD, S. and VANDENBERGHE, L. (2004). Convex Optimization. Cambridge Univ. Press. MR2061575
3. COHEN, A. (2003). Numerical Analysis of Wavelet Methods. North-Holland, Amsterdam. MR1990555
4. DAUBECHIES, I. (1992). Ten Lectures on Wavelets. SIAM, Philadelphia. MR1162107
5. FAŸ, G., ROUEFF, F. and SOULIER, P. (2007). Estimation of the memory parameter of the infinite-source Poisson process. Bernoulli. 13 473-491. MR2331260
6. GEWEKE, J. and PORTER-HUDAK, S. (1983). The estimation and application of long memory time series models. J. Time Ser. Anal. 4 221-238. MR0738585
7. GIRAITIS, L., ROBINSON, P. M. and SAMAROV, A. (1997). Rate optimal semiparametric estimation of the memory parameter of the Gaussian time series with long range dependence. J. Time Ser. Anal. 18 49-61. MR1437741
8. HURVICH, C. M., MOULINES, E. and SOULIER, P. (2002). The FEXP estimator for potentially nonstationary linear time series. Stoch. Proc. App. 97 307-340. MR1875337
9. HURVICH, C. M. and RAY, B. K. (1995). Estimation of the memory parameter for nonstationary or noninvertible fractionally integrated processes. J. Time Ser. Anal. 16 17-41. MR1323616
10. KAPLAN, L. M. and KUO, C.-C. J. (1993). Fractal estimation from noisy data via discrete fractional Gaussian noise (DFGN) and the Haar basis. IEEE Trans. Signal Process. 41 3554-3562.
11. KÜNSCH, H. R. (1987). Statistical aspects of self-similar processes. In Probability Theory and Applications. Proc. World Congr. Bernoulli Soc. 1 67-74. VNU Sci. Press, Utrecht. MR1092336
12. MCCOY, E. J. and WALDEN, A. T. (1996). Wavelet analysis and synthesis of stationary long-memory processes. J. Comput. Graph. Statist. 5 26-56. MR1380851
13. MOULINES, E., ROUEFF, F. and TAQQU, M. S. (2006). Central Limit Theorem for the logregression wavelet estimation of the memory parameter in the Gaussian semi-parametric context. Fractals 15 301-313.
14. MOULINES, E., ROUEFF, F. and TAQQU, M. S. (2007). On the spectral density of the wavelet coefficients of long memory time series with application to the log-regression estimation of the memory parameter. J. Time Ser. Anal. 28. MR2345656
15. ROBINSON, P. M. (1995). Gaussian semiparametric estimation of long range dependence. Ann. Statist. 23 1630-1661. MR1370301
16. ROBINSON, P. M. (1995). Log-periodogram regression of time series with long range dependence. Ann. Statist. 23 1048-1072. MR1345214
17. ROBINSON, P. M. and HENRY, M. (2003). Higher-order kernel semiparametric M-estimation of long memory. J. Econometrics 114 1-27. MR1962371
18. ROSENBLATT, M. (1985). Stationary Sequences and Random Fields. Birkhäuser, Boston. MR0885090
19. ROUGHAN, M., VEITCH, D. and ABRY, P. (2000). Real-time estimation of the parameters of long-range dependence. IEEE/ACM Transactions on Networking 8 467-478.
20. SHIMOTSU, K. and PHILLIPS, P. C. B. (2005). Exact local Whittle estimation of fractional integration. Ann. Statist. 33 1890-1933. MR2166565
21. VAN DER VAART, A. W. (1998). Asymptotic Statistics. Cambridge Univ. Press. MR1652247
22. VELASCO, C. (1999). Gaussian semiparametric estimation of non-stationary time series. J. Time Ser. Anal. 20 87-127. MR1678573
23. WORNELL, G. W. and OPPENHEIM, A. V. (1992). Estimation of fractal signals from noisy measurements using wavelets. IEEE Trans. Signal Process. 40 611-623.