Broadband log-periodogram regression of time series with long-range dependence

Annals of Statistics

Volumn 27, Issue 4, 1999, Pages 1415-1439

  Moulines, Eric ^a   Soulier, Philippe ^b  

^a CNRS   (France)

^b UNIVERSITÉ D EVRY VAL D ESSONNE   (France)

Author keywords

Central limit theorems for dependent variables; Log periodogram regression; Long range dependence

Indexed keywords

EID: 0033236911     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1017938932     Document Type: Article

References (21)

1. ARCONES, M. (1994). Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors. Ann. Probab. 22 2243-2274.
2. BERAN, J. (1993). Fitting long memory models by generalized regression. Biometrika 80 817-822.
3. BERAN, J. (1994). Statistics for long memory processes. Chapman and Hall, New York.
4. DAHLHAUS, R. (1989). Efficient parameter estimation for self-similar processes. Ann. Statist. 17 1749-1766.
5. FOX, R. and TAQQU, M. S. (1986). Large samples properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann. Statist. 14 517-532.
6. GEWEKE, J. and PORTER-HUDAK, S. (1983). The estimation and application of long memory time series models. J. Time Anal. 4 221-238.
7. GIRAITIS, L., ROBINSON, P. and SAMAROV, A. (1997). Rate optimal semiparametric estimation of the memory parameter of the Gaussian time series with long range dependence. J. Time Series Anal. 18 49-61.
8. GIRAITIS, L. and SURGAILIS, D. (1990). A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotic normality of Whittles's estimate. Probab. Theory Related Fields 86 87-104.
9. GRANGER, C. W. J. and JOYEUX, R. (1980). An introduction to long memory time series and fractional differencing. J. Time Series Anal. 1 15-30.
10. HART, J. D. (1997). Nonparametric smoothing and lack-of-fit tests. Springer Series in Statistics. New York, NY: Springer.
11. HURVICH, C. and BELTRAO, K. (1993). Asymptotics of the low-frequency ordinates of the periodogram of a long-memory time series. J. Time Series Anal. 14 455-472.
12. HURVICH, C., DEO, R. and BRODSKY, J. (1998). The mean squared error of Geweise and Porter-Hudak's estimator of a long-memory time-series. J. Time Ser. Anal. 19 19-46.
13. JOHNSON, N. L. and KOTZ, S. (1970). Continuous Univariate Distributions 1 Wiley, New York.
14. KÜNSCH, H. R. (1986). Discrimination between monotonic trends and long-range dependence. J. Appl. Probab. 23 1025-1030.
15. MOULINES, E. and SOULIER, P. (1998). Data-driven order selection for long range dependent time series. J. Time Ser. Anal. To appear.
16. ROBINSON, P. M. (1994). Time series with strong dependence. In Advances in Econometrics. Proceedings of the Sixth World Congress 1 47-95. Cambridge Univ. Press.
17. ROBINSON, P. M. (1995a). Log-periodogram regression of time series with long range dependence. Annal. Statist. 23 1048-1072.
18. ROBINSON, P. M. (1995b). Gaussian semi-parametric estimation of long range dependence. Annal. Statist. 23 1630-1661.
19. SOULIER, P. (1998). Some new bounds and a central limit theorem for nonstationary sequences of Gaussian vectors. Université d'Evry-Val d'Essonne. Submitted to Statistics and Probability Letters.
20. TAQQU, M. S. (1977). Law of the iterated logarithm for sums of nonlinear functions of Gaussian variables that exhibit long range dependence. Z. Wahrsch. Verw. Gebiete. 40 203-238.
21. VELASCO, C. (1999). Gaussian semiparametric estimation of non-stationary time series. J. Time Ser. Anal. 20 87-127.