Multiple local whittle estimation in stationary systems

Annals of Statistics

Volumn 36, Issue 5, 2008, Pages 2508-2530

  Robinson, P M ^a  

^a LONDON SCHOOL OF ECONOMICS   (United Kingdom)

Author keywords

Asymptotic normality; Cointegration; Consistency; Long memory; Phase; Semiparametric estimation

Indexed keywords

EID: 54349113803     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/07-AOS545     Document Type: Article

References (38)

1. ADENSTEDT, R. (1974). On large-sample estimation for the mean of a stationary random sequence. Ann. Statist. 2 1095-1107.
2. ANDERSON, T. W. and WALKER, A. M. (1964). On the asymptotic distribution of the autocorrelations of a sample from a linear stochastic process. Ann. Math. Statist. 35 1296-1303.
3. BREIDT, F. J., DAVIS, R. A. and TRINDADE, A. A. (2001). Least absolute deviation estimation for all-pass time series models. Ann. Statist. 29 919-946.
4. BRILLINGER, D. R. (1975). Time Series. Data Analysis and Theory. Holt, Rinehart and Winston, New York.
5. CHEN, W. W. and HURVICH, C. M. (2006). Semiparametric estimation of fractional cointegrating subspaces. Ann. Statist. 34 2939-2979.
6. CHRISTENSEN, B. J. and NIELSEN, M. (2006). Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting. J. Econometrics 133 343-371.
7. DAHLHAUS, R. (1989). Efficient parameter estimation for self-similar processes. Ann. Statist. 17 1749-1766.
8. DAVIDSON, J. E. H. and HASHIMADZE, N. (2008). Alternative frequency and time domain versions of fractional Brownian motion. Econometric Theory 24 256-297.
9. FOX, R. and TAQQU, M. S. (1986). Large-sample properties of parameter estimates for strongly dependent stationary Gaussian series. Ann. Statist. 14 517-532.
10. GIRAITIS, L. and ROBINSON, P. M. (2003). Edgeworth expansions for semiparametric Whittle estimation of long memory. Ann. Statist. 31 1325-1375.
11. 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 Whittle's estimate. Probab. Theory Related Fields 86 87-104.
12. HANNAN, E. J. (1970). Multiple Time Series. Wiley, New York.
13. 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 II. Lecture Notes in Statist. 115 220-232. Springer, New York.
14. HOSOYA, Y. (1997). Limit theory with long-range dependence and statistical inference of related models. Ann. Statist. 25 105-137.
15. HUALDE, J. and ROBINSON, P. M. (2004). Semiparametric estimation of fractional cointegration. Preprint, London School of Economics.
16. HURVICH, C. M. and BELTRAO, K. J. (1994). Automatic semiparametric estimation of the memory parameter of a long memory time series. J. Time Ser. Anal. 15 285-302.
17. HURVICH, C. M. and DEO, R. S. (2001). Plug-in selection of the number of frequencies in regression estimates of the memory parameter of long memory time series. J. Time Ser. Anal. 20 331-341.
18. HURVICH, C. M., MOULINES, E. and SOULIER, E. (2005). Estimating long memory in volatility. Econometrica 73 1283-1328.
19. JOHANSEN, S. (2005). A representation theory for a class of vector autoregressive models for fractional processes. Working paper, Dept. Applied Mathematics and Statistics, Univ. Copenhagen.
20. KÜNSCH, H. R. (1987). Statistical aspects of self-similar processes. In Proceedings of the First World Congress of the Bernoulli Society 1 67-74. VNU Sci. Press, Utrecht.
21. LII, K. S. and ROSENBLATT, M. (1982). Deconvolution and estimation of transfer function phase and coefficients for non-Gaussian linear processes. Ann. Statist. 10 1195-1208.
22. LOBATO, I. N. (1999). A semiparametric two-step estimator in a multivariate long memory model. J. Econometrics 90 129-153.
23. NIELSEN, M. O. (2005). Semiparametric estimation in time-series regression with long-range dependence. J. Time Ser. Anal. 26 279-304.
24. NIELSEN, M. O. (2007). Local Whittle analysis of stationary fractional cointegration and the implied-realized volatility relation. J. Bus. Econ. Statist. 25 427-446.
25. PARZEN, E. (1957). A central limit theorem for multilinear stochastic process. Ann. Math. Statist. 28 252-256.
26. PHILLIPS, P. C. B. and SHIMOTSU, K. (2004). Whittle estimation in nonstationary and unit root cases. Ann. Statist. 32 656-672.
27. ROBINSON, P. M. (1994). Semiparametric analysis of long-memory time series. Ann. Statist. 22 515-539.
28. ROBINSON, P. M. (1995). Log-periodogram regression of time series with long range dependence. Ann. Statist. 23 1048-1072.
29. ROBINSON, P. M. (1995). Gaussian semiparametric estimation of long range dependence. Ann. Statist. 23 1630-1661.
30. ROBINSON, P. M. (2005). Robust covariance matrix estimation: "HAC" estimates with long memory/antipersistence correction. Econometric Theory 21 171-180.
31. ROBINSON, P. M. and MARINUCCI, D. (2001). Narrow-band analysis of nonstationary processes. Ann. Statist. 29 947-986.
32. ROBINSON, P. M. and MARINUCCI, D. (2003). Semiparametric frequency-domain analysis of fractional cointegration. In Time Series with Long Memory. Adv. Texts Econometrics 334-373. Oxford Univ. Press.
33. SHIMOTSU, K. (2007). Gaussian semiparametric estimation of multivariate fractionally integrated processes. J. Econometrics 137 277-310.
34. SHIMOTSU, K. and PHILLIPS, P. C. B. (2006). Exact local Whittle estimation of fractional integration. Ann. Statist. 33 1890-1933.
35. VELASCO, C. (1999). Gaussian semiparametric estimation of non-stationary time series. J. Time Ser. Anal. 20 87-127.
36. VELASCO, C. (2000). Gaussian semi-parametric estimation of fractional cointegration. Preprint, Univ. Carlos III de Madrid.
37. VELASCO, C. (2003). Gaussian semi-parametric estimation of fractional cointegration. J. Time Ser. Anal. 24 345-378.
38. ZYGMUND, A. A. (1977). Trigonometric Series. I, II. Cambridge Univ. Press, New York.