Asymptotic theory for maximum likelihood estimation of the memory parameter in stationary Gaussian processes

Econometric Theory

Volumn 28, Issue 2, 2012, Pages 457-470

  Lieberman, Offer ^a   Rosemarin, Roy ^b   Rousseau, Judith ^c  

^a UNIVERSITY OF HAIFA   (Israel)

^b LONDON SCHOOL OF ECONOMICS   (United Kingdom)

^c UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84859119148     PISSN: 02664666     EISSN: 14694360     Source Type: Journal    
DOI: 10.1017/S0266466611000399     Document Type: Article

References (34)

1. Abadir, K.M., W. Distaso, & L. Giraitis (2007) Nonstationarity- extended local Whittle estimation. Journal of Econometrics 141, 1353-1384.
2. Adenstedt, R.K. (1974) On large-sample estimation for the mean of a stationary random sequence. Annals of Statistics 2, 1095-1107.
3. Beran, J. (1991) M-estimator of location for data with slowly decaying serial correlations. Journal of the American Statistical Association 86, 704-708.
4. Beran, J., Y. Feng, G. Franke, D. Hess, & D. Ocker (2003) Semiparametric modeling of stochastic and deterministic trends and fractional stationarity. In G. Rangarajan &M. Ding, (eds.) Processes with Long Range Correlations: Theory and Applications, pp. 225-250. Springer.
5. Cheung, Y.W. & F.X. Diebold (1994) On maximum likelihood estimation of the differencing parameter of fractionally integrated noise with unknown mean. Journal of Econometrics 62, 301-316.
6. Dahlhaus, R. (1989) Efficient parameter estimation for self-similar processes. Annals of Statistics 17, 1749-1766.
7. Dahlhaus, R. (2006) Correction note: Efficient parameter estimation for self-similar processes. Annals of Statistics 34, 1045-1047.
8. Fox, R. & M.S. Taqqu (1986) Large sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Annals of Statistics 14, 157-532.
9. Fox, R. & M.S. Taqqu (1987) Central limit theorems for quadratic forms in random variables having long-range dependence. Probability Theory and Related Fields 74, 213-240.
10. Granger, C.W.J. & R. Joyeux (1980) An introduction to long-range time series models and fractional differencing. Journal of Time Series Analysis 1, 15-31.
11. Hannan, E.J. (1973) The asymptotic theory of linear time series models. Journal of Applied Probability 10, 130-145.
12. Hauser, M.A. (1999) Maximum likelihood estimators for ARMA and ARFIMA models: A Monte Carlo study. Journal of Statistical Planning and Inference 80, 229-255.
13. Hosking, J.R.M. (1981) Fractional differencing. Biometrika 68, 165-176.
14. Karuppiah, J. & C.A. Los (2005)Wavelet multiresolution analysis of high-frequency Asian FX rates, summer 1997. International Review of Financial Analysis 14, 211-246.
15. Lieberman, O. & P.C.B. Phillips (2004) Expansions for the distribution of the maximum likelihood estimator of the fractional difference parameter. Econometric Theory 20, 464-484.
16. Lieberman, O., R. Rosemarin, & J. Rousseau (2010) Asymptotic Theory for Maximum Likelihood Estimation of the Memory Parameter in Stationary Gaussian Processess (full version). Available at http://www.ceremade.dauphine.fr/ rousseau/LRRlongmemo.html.
17. Mandelbrot, B.B. & J.W. Van Ness (1968) Fractional Brownian motions, fractional noises and applications. SIAM Review 10, 422-37.
18. Nielsen, M. & P.H. Frederiksen (2005) Finite sample comparison of parametric, semiparametric, and wavelet estimators of fractional integration. Econometric Reviews 24, 405-443.
19. Peters, E.E. (1994) Fractal Market Analysis: Applying Chaos Theory to Investment and Economics. Wiley.
20. Polard, D. (1984) Convergence of Stochastic Processes. Wiley.
21. Robinson, P.M. (1995a) Gaussian semiparametric estimation of long-range dependence. Annals of Statistics 23, 1630-1661.
22. Robinson, P.M. (1995b) Log-periodogram regression of time series with long range dependence. Annals of Statistics 23, 1048-1072.
23. Samarov, A. & M.S. Taqqu (1988) On the efficiency of the sample mean in long-memory noise. Journal of Time Series Analysis 9, 191-200.
24. Shao, X. (2010) Nonstationarity-extended Whittle estimation. Econometric Theory 26, 1060-1087.
25. Shimotsu, K. (2010) Exact local Whittle estimation of fractional integration with unknown mean and time trend. Econometric Theory 26, 501-540.
26. Shimotsu, K. & P.C.B. Phillips (2004) Exact local Whittle estimation of fractional integration. Annals of Statistics 33, 1890-1933.
27. Shiryaev, A.N. (1999) Essentials of Stochastic Finance: Facts, Models, Theory.World Scientific.
28. Sowell, F.B. (1992) Maximum likelihood estimation of stationary univariate fractionally integrated time series models. Journal of Econometrics 53, 165-188.
29. Terrin, N. & M.S. Taqqu (1990) A noncentral limit theorem for quadratic forms of Gaussian stationary sequences. Journal of Theoretical Probability 3, 449-475.
30. Tsai, H. (2009) On continuous-time autoregressive fractionally integrated moving average processes. Bernoulli 15, 178-194.
31. Velasco, C. (1999a) Gaussian semiparametric estimation of nonstationary time series. Journal of Time Series Analysis 20, 87-127.
32. Velasco, C. (1999b) Non-stationary log-periodogram regression. Journal of Econometrics 91, 325-371.
33. Velasco, C. & P.M. Robinson (2000) Whittle pseudo-maximum likelihood estimation for nonstationary time series. Journal of the American Statistical Association 95, 1229-1243.
34. Yajima, Y. (1985) On estimation of long-memory time series models. Australian Journal of Statistics 27, 303-20.