Data driven order selection for projection estimator of the spectral density of time series with long range dependence

Journal of Time Series Analysis

Volumn 21, Issue 2, 2000, Pages 193-218

  Moulines, Eric ^a   Soulier, Philippe ^b  

^a TELECOM PARISTECH   (France)

^b UNIVERSITÉ D EVRY VAL D ESSONNE   (France)

Author keywords

Data driven order selection; Fractional exponential models; Log periodogram regression; Long range dependence; Projection estimator

Indexed keywords

EID: 0000893842     PISSN: 01439782     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9892.00181     Document Type: Article

References (30)

1. AGIAKLOGLOU, C., NEWBOLD, P. and WOHAR, M. (1993) Bias in an estimator of the fractional difference parameter, Journal of Time Series Analysis, 14, pp. 235-246.
2. BERAN, J. (1993) Fitting long memory models by generalized regression, Biometrika, 80, pp. 817-822.
3. _ (1994) Statistics for long-memory processes, Chapman & Hall, 1994.
4. BLOOMFIELD, P. (1973) An exponential model for the spectrum of scalar time series, Biometrika, 60, pp. 217-226.
5. CHEUNG, Y. and DIEBOLD, F. (1994) On maximum likelihood estimation of the differencing parameter of fractionally integrated noise with unknown mean, J. of Econometrics, 62 (1994), pp. 301-316.
6. DAHLHAUS, R. (1989) Efficient parameter estimation for self-similar processes, The Annals of Statistics, 17, pp. 1749-1766.
7. Fox, R. and TAQQU, M. (1986) Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time-series, The Annals of Statistics, 14, pp. 517-532.
8. GEWEKE, J. and PORTER-HUDAK, S. (1983) The estimation and application of long-memory time-series models, Journal of Time Series Analysis, 4, pp. 221-238.
9. GIRAITIS, L., ROBINSON, P. and SAMAROV, A. (1997) Rate optimal semi-parametric estimation of the memory parameter of the gaussian time series long-range dependence, Journal of Time Series Analysis, 18, pp. 49-60.
10. _ and SURGAILIS, D. (1990) A central-limit theorem for quadratic forms in strongly dependent linear variables and application to asymptotical normality of whittle estimate, Probability Theory and Related Fields, 86, pp. 87-104.
11. HART, J. (1997) Non parametric smoothing and lack-of-fit tests, Springer Series in Statistics, Springer-Verlag.
12. HURVICH, C. and BELTRAO, K. (1993) Asymptotics for the low-frequency ordinates of the periodogram of a long-memory times series, Journal of Time Series Analysis, 14, pp. 455-472.
13. KOOPERBERG, C., STONE, C. and TRUONG, Y. (1995a) Log-spline estimation of a possibly mixed spectral distribution, Journal of Time Series Analysis, 16, pp. 359-388.
14. _ (1995b) Rate of convergence for log-spline spectral density estimation, Journal of Time Series Analysis, 16, pp. 389-401.
15. KUNSCH, H. (1986) Discrimination between monotonic trends and long-range dependence, Journal of Applied Probability, 23, pp. 1025-1030.
16. l, cross-validation and generalized cross-validation: discrete time index, The Annals of Statistics, 15, pp. 958-975.
17. MORICZ, E, SERFLING, R. and STOUT, W. (1982) Moments and probability bounds with quasi-super additive structure for the maximum of partial sums, Annals of Probability, 4, pp. 1032-1040.
18. MOULINES, E. and SOULIER, P. H. (1999) Broadband log-periodogram regression of time series with long range dependence (en collaboration avec Eric Moulines). The Annals of Statistics, 27, No. 4.
19. POLYAK, B. and TSYBAKOV, A. (1989) Asymptotic optimality of the cp test for the orthogonal series estimation of regression, Theory of Probability and Their Applications, 35 (1989), pp. 293-306.
20. REISEN, V (1994) Estimation of the fractional difference parameter in the ARFIMA(p, d, q) model using smoothed periodogram, Journal of Time Series Analysis, 15 (1994), pp. 335-350.
21. ROBINSON, P. (1991), Nonparametric and semi-parametric methods in econometrics and statistics, in Proceedings of the Fifth International symposium in economic theory and econometrics, W. Barnett, J. Powell, and G. Tauchen, eds., 1991, pp. 437-457.
22. _ (1994a) Time series with strong dependence, vol. 1, Cambridge University Press, 1994, ch. 2 of Advances in Econometrics, Sixth World Congress, pp. 47-95.
23. _ (1994b) Semiparametric analysis of long-memory time series, The Annals of Statistics, 22 (1994), pp. 515-539.
24. _ (1995a) Gaussian semi-parametric estimation of long-range dependence, The Annals of Statistics, 23, pp. 1630-1661.
25. _ (1995b) Log-periodogram regression of time-series with long-range dependence, The Annals of Statistics, 23, pp. 1630-1661.
26. SMITH, J., TAYLOR, N. and YADAV, S. (1997) Comparing the bias and misspecification in ARFIMA models, Journal of Time Series Analysis, 18, pp. 507-527.
27. SOULIER, P. (1998) Some new bounds and a central limit theorem for non stationary sequences of gaussian vectors, tech. rep., Université d'Evry-Val d'Essonne.
28. SOWELL, E (1992), Maximum likelihood estimation of stationary univariate fractionally integrated time series models, Journal of Econometrics, 53, pp. 165-188.
29. TAQQU, M. and TEVEROVSKI, V (1996) Semi-parametric graphical estimation techniques for long-memory data, in Proceedings of the Athens Conference on Applied Probability and Time-Series Analysis, vol. 115 of Lecture Notes in Statistics, Springer-Verlag, pp. 420-432.
30. _ (1997) Robustness of whittle-type estimators of time-series with long-range dependence, Communications in Statistics: Stochastic Models.