On the Kullback-Leibler information divergence of locally stationary processes1

Stochastic Processes and their Applications

Volumn 62, Issue 1, 1996, Pages 139-168

  Dahlhaus, R ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

Evolutionary spectra; Kullback leibler divergence; Locally stationary processes; Time varying autoregressions

Indexed keywords

EID: 0030095346     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/0304-4149(95)00090-9     Document Type: Article

References (24)

1. N.K. Bary, A Treatise on Trigonometric Series, Vol. I (Pergamon, Oxford, 1964).
2. P. Brockwell and R.A. Davis, Time Series: Theory and Methods (Springer, New York, 1987).
3. L. Cohen, Time-frequency distributions - a review. Proc. IEEE 77 (1989) 941-981.
4. R. Dahlhaus, Fitting time series models to nonstationary processes, Beiträge zur Statistik No. 4, (Universität Heidelberg, 1993).
5. R. Dahlhaus, Maximum likelihood estimation and model selection for nonstationary processes, J. Nonparametric Statist. 6 (1996a) to appear.
6. R. Dahlhaus, Asymptotic statistical inference for nonstationary processes with evolutionary spectra. Preprint, Universität Heidelberg (1996b).
7. R.B. Davies, Asymptotic inference in stationary Gaussian time-series, Adv. Appl. Probab. 5 (1973) 469-497.
8. F.A. Graybill, Matrices with Applications in Statistics (Wadsworth. Belmont, California, 2nd ed., 1983).
9. M. Hallin, Mixed autoregressive moving-average multivariate processes with time-dependent coefficients, J Multivariate Anal. 8 (1978) 567-572.
10. M. Hallin, Nonstationary q-dependent processes and time-varying moving average models: invertibility properties and the forecasting problem, Adv. Appl. Probab. 18 (1986) 170-210.
11. G. Kitagawa and W. Gersch, A smoothness priors time-varying AR coefficient modeling of nonstationary covariance time series, IEEE Trans. Automat. Control, AC 30 (1985) 48-56.
12. H.R. Künsch, A note on causal solutions for locally stationary AR processes, preprint (ETH Zürich, 1995).
13. W. Martin and P. Flandrin, Wigner-Ville spectral analysis of nonstationary processes, IEEE Trans. Acoust. Speech Signal Process. 33 (1985) 1461-1470.
14. G. Mélard, An example of the evolutionary spectrum theory, J. Time Ser. Anal. 6 (1985) 81-90.
15. G. Mélard and A. Harteleer-de Schutter, Contributions to evolutionary spectral theory, J. Time Ser. Anal. 10 (1989) 41-63.
16. K.S. Miller, Linear Difference Equations (Benjamin, New York, 1968).
17. E. Parzen, in: D.R. Brillinger, P.R. Krishnaiah, eds., Handbook of Statistics, Vol. 3, (Elsevier, Amsterdam 1983) pp. 221-247.
18. M.B. Priestley, Evolutionary spectra and non-stationary processes, J. Roy. Statist. Soc. Ser. B 27 (1965) 204-237.
19. M.B. Priestley, Spectral Analysis and Time Series, Vol. 2, (Academic Press, London, 1981).
20. P.M. Robinson, Nonparametric estimation of time-varying parameters, in: P. Hackl, ed., Statistical Analysis and Forecasting of Economic Structural Change (Springer, Berlin, 1989) pp. 253-264.
21. T. Subba Rao, Discussion on the paper by Priestley and Tong "On the analysis of bivariate non-stationary processes (153-166)", J.S. Roy. Statist. Soc. Ser. B 35 (1973) 182-183.
22. P.J. Thomson and P. de Souza, P., in: E.J. Hannan, P.R. Krishnaiah, M.M. Rao, eds., Handbook of Statistics, Vol. 5 (Elsevier, Amsterdam, 1985) pp. 389-412.
23. D. Tjøstheim, Spectral generating operators for non-stationary processes, Adv. Appl. Probab 8 (1976) 831-846.
24. P. Whittle, Estimation and information in stationary time series, Ark. Mat. 2 (1953) 423-434.