Edgeworth expansions for semiparametric Whittle estimation of long memory

Annals of Statistics

Volumn 31, Issue 4, 2003, Pages 1325-1375

  Giraitis, L ^a   Robinson, P M ^a  

^a LONDON SCHOOL OF ECONOMICS   (United Kingdom)

Author keywords

Edgeworth expansion; Long memory; Semiparametric estimation

Indexed keywords

EID: 0041857892     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1059655915     Document Type: Article

References (32)

1. ANDREWS, D. W. K. and GUGGENBERGER, P. (2003). A bias-reduced log-periodogram regression estimator for the long memory parameter. Econometrica 71 675-712.
2. ANDREWS, D. W. K. and SUN, Y. (2001). Local polynomial Whittle estimation of long range dependence. Preprint. Cowles Foundation for Research in Economics, Yale Univ.
3. BENTKUS, R. Y. and RUDZKIS, R. A. (1982). On the distribution of some statistical estimates of a spectral density. Theory Probab. Appl. 27 795-814.
4. BHATTACHARYA, R. N. and GHOSH, J. K, (1978). On the validity of the formal Edgeworth expansion. Ann. Statist. 6 434-451.
5. BHATTACHARYA, R. N. and RANGA RAO, R. (1976). Normal Approximation and Asymptotic Expansions. Wiley, New York.
6. BRILLINGER, D. R. (1975). Time Series: Data Analysis and Theory. Holden Day, San Francisco.
7. CHIBISOV, D. M. (1972). An asymptotic expansion for the distribution of a statistic admitting an asymptotic expansion. Theory Probab. Appl. 17 620-630.
8. FOX, R. and TAQQU, M. S. (1986). Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann. Statist. 14 517-532.
9. GEWEKE, J. and PORTER-HUDAK, S. (1983). The estimation and application of long memory time series models. J. Time Ser. Anal. 4 221-238.
10. 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 49-60.
11. GIRAITIS, L., ROBINSON, P. M. and SAMAROV, A. (2000). Adaptive semiparametric estimation of the memory parameter. J. Multivariate Anal. 72 183-207.
12. HALL, P. (1991). Edgeworth expansions for nonparametric density estimators, with applications. Statistics 22 215-232.
13. HANNAN, E. J. (1973). The asymptotic theory of linear time series models. J. Appl. Probab. 10 130-145.
14. HENRY, M. and ROBINSON, P. M. (1996). Bandwidth choice in Gaussian semiparametric estimation of long range dependence. Athens Conference on Applied Probability and Time Series Analysis. Time Series Analysis. Lecture Notes in Statist. 115 220-232. Springer, New York.
15. HURVICH, C. M. and BRODSKY, J. (2001). Broadband semiparametric estimation of the memory parameter of a long memory time series using fractional exponential models. J. Time Ser. Anal 22 221-249.
16. HURVICH, C. M. and CHEN, W. W. (2000). An efficient taper for potentially overdifferenced long memory time series. J. Time Ser. Anal. 21 155-180.
17. HURVICH, C. M. and RAY, B. (1995). Estimation of the memory parameter for nonstationary or noninvertable fractionally integrated processes. J. Time Ser. Anal. 16 17-42.
18. IBRAGIMOV, I. A. and HAS'MINSKII, R. Z. (1981). Statistical Estimation. Asymptotic Theory. Springer, New York.
19. JANACEK, G. J. (1982). Determining the degree of differencing for time series via the log spectrum. J. Time Ser. Anal. 3 177-183.
20. KÜNSCH, H. (1987). Statistical aspects of self-similar processes. In Proc. First World Congress of the Bernoulli Society (Yu. A. Prokhorov and V. V. Sazonov, eds.) 1 67-74. VNU Science Press, Utrecht.
21. LIEBERMAN, O., ROUSSEAU, J. and ZUCKER, D. M. (2001). Valid Edgeworth expansion for the sample autocorrelation function under long range dependence. Econometric Theory 17 257-275.
22. MOULINES, E, and SOULIER, P. (1999). Broadband log-periodogram regression of time series with long range dependence. Ann. Statist. 27 1415-1439.
23. NISHIYAMA, Y. and ROBINSON, P. M. (2000). Edgeworth expansions for semiparametric averaged derivatives. Econometrica 68 931-979.
24. ROBINSON, P. M. (1995a). Log-periodogram regression of time series with long range dependence. Ann. Statist. 23 1048-1072.
25. ROBINSON, P. M. (1995b). Gaussian semiparametric estimation of long range dependence. Ann. Statist. 23 1630-1661.
26. ROBINSON, P. M. (1995c). The approximate distribution of nonparametric regression estimates. Statist. Probab. Lett. 23 193-201.
27. ROBINSON, P. M. and HENRY, M. (1999). Long and short memory conditional heteroscedasticity in estimating the memory parameter of levels. Econometric Theory 15 299-336.
28. ROBINSON, P. M. and HENRY, M. (2003). Higher-order kernel semiparametric M -estimation of long memory. J. Econometrics 114 1-27.
29. TANIGUCHI, M. (1991). Higher-Order Asymptotic Theory for Time Series Analysis. Lecture Notes in Statist. 68. Springer, New York.
30. VELASCO, C. (1999a). Nonstationary log-periodogram regression. J. Econometrics 91 325-371.
31. VELASCO, C. (1999b). Gaussian semiparametric estimation of nonstationary time series. J. Time Ser. Anal 20 87-127.
32. VELASCO, C. and ROBINSON, P. M. (2001). Edgeworth expansions for spectral density estimates and studentized sample mean. Econometric Theory 17 497-539.