A likelihood approximation for locally stationary processes

Annals of Statistics

Volumn 28, Issue 6, 2000, Pages 1762-1794

  Dahlhaus, Rainer ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

Generalized Toeplitz matrices; Local likelihood; Locally stationary; Preperiodogram; Whittle likelihood

Indexed keywords

EID: 0034343455     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1015957480     Document Type: Article

References (28)

1. BRILLINGER, D. R. (1981). Time Series: Data Analysis and Theory. Holden-Day, San Francisco.
2. DAHLHAUS, R. (1996a). On the Kullback-Leibler information divergence of locally stationary processes. Stochastic Process. Appl. 62 139-168.
3. DAHLHAUS, R. (1996b). Maximum likelihood estimation and model selection for locally stationary processes. J. Nonparametr. Statist. 6 171-191.
4. DAHLHAUS, R. (1996c). Asymptotic statistical inference for nonstationary processes with evolutionary spectra. Athens Conference on Applied Probability and Time Series 2. Lecture Notes in Statist. 115 145-159. Springer, New York.
5. DAHLHAUS, R. (1997). Fitting time series models to nonstationary processes. Ann. Statist. 25 1-37.
6. DAHLHAUS, R. and NEUMANN, M. H. (2000). Locally adaptive fitting of semiparametric models to nonstationary time series. Stochastic Process. Appl. To appear.
7. DAVIES, R. B. (1973). Asymptotic inference in stationary Gaussian time series. Adv. in Appl. Probab. 5 469-497.
8. DUNSMUIR, W. (1979). A central limit theorem for parameter estimation in stationary vector time series and its application to models for a signal observed with noise. Ann. Statist. 7 490-506.
9. DZHAPARIDZE, K. (1971). On methods for obtaining asymptotically efficient spectral parameter estimates for a stationary Gaussian process with rational spectral density. Theory Probab. Appl. 16 550-554.
10. DZHAPARIDZE, K. (1986). Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series. Springer, New York.
11. 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.
12. GRANGER, C. W. J. and HATTANAKA, M. (1964). Spectral Analysis of Econometric Time Series. Princeton Univ. Press.
13. GRAYBILL, F. A. (1983). Matrices with Applications in Statistics. Wadsworth, Belmont, CA.
14. GRENANDER, U. and SZEGÖ, G. (1958). Toeplitz Forms and Their Applications. Univ. California Press, Berkeley.
15. HANNAN, E. J. (1973). The asymptotic theory of linear time series models. J. Appl. Probab. 10 130-145.
16. HANNAN, E. J. and DEISTLER, M. (1988). The Statistical Theory of Linear Systems. Wiley, New York.
17. HOSOYA, Y. and TANIGUCHI, M. (1982). A central limit theorem for stationary processes and the parameter estimation of linear processes. Ann. Statist. 10 132-153.
18. MALLAT, S., PAPANICOLAOU, G. and ZHANG, Z. (1998). Adaptive covariance estimation of locally stationary processes. Ann. Statist. 26 1-47.
19. MIKOSCH, T., GADRICH, T., KLÜPPELBERG, C. and ADLER, R. J. (1995). Parameter estimation for ARMA models with infinite variance innovations. Ann. Statist. 23 305-326.
20. NEUMANN, M. H. and VON SACHS, R. (1997). Wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra. Ann. Statist. 25 38-76.
21. PARZEN, E. (1983). Autoregressive spectral estimation. In Handbook of Statistics (D. R. Brillinger and P. R. Krishnaiah, eds.) 3 221-247. North-Holland, Amsterdam.
22. PRIESTLEY, M. B. (1965). Evolutionary spectra and nonstationary processes. J. Roy. Statist. Soc. Ser. B 27 204-237.
23. PRIESTLEY, M. B. (1981). Spectral Analysis and Time Series. 2. Academic Press, London.
24. ROBINSON, P. M. (1995). Gaussian semiparametric estimation of long range dependence. Ann. Statist. 23 1630-1661.
25. STRASSER, H. (1985). Mathematical Theory of Statistics, de Gruyter, Berlin.
26. TANIGUCHI, M. (1983). On the second order asymptotic efficiency of estimators of Gaussian ARMA processes. Ann. Statist. 11 157-169.
27. WHITTLE, P. (1953). Estimation and information in stationary time series. Ark. Mat. 2 423-434.
28. WHITTLE, P. (1954). Some recent contributions to the theory of stationary processes. In A Study in the Analysis of Stationary Time Series, 2nd ed. (H. Wold, ed.) 196-228. Almqvist and Wiksell, Uppsala.