×

zbMATH — the first resource for mathematics

Maximum likelihood estimation and model selection for locally stationary processes. (English) Zbl 0879.62025
Summary: The Gaussian maximum likelihood estimate is investigated for time series models that have locally a stationary behaviour (e.g. for time varying autoregressive models). The asymptotic properties are studied in the case where the fitted model is either correct or misspecified. For example the behaviour of the maximum likelihood estimate is explained in the case where a stationary model is fitted to a nonstationary process. As a general model selection criterion the AIC is considered. It can for example automatically select between stationary models, nonstationary models and deterministic trends.

MSC:
62G05 Nonparametric estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G20 Asymptotic properties of nonparametric inference
PDF BibTeX Cite
Full Text: DOI
References:
[1] DOI: 10.1109/TAC.1974.1100705 · Zbl 0314.62039
[2] Azencott R., Forecasting and Model Building (1986) · Zbl 0593.62088
[3] Brillinger D. R., Time Series: Data Analysis and Theory (1981) · Zbl 0486.62095
[4] Brockwell P., Time Series: Theory and Methods (1987)
[5] Dahlhaus R. Fitting time series models to nonstationary process Beiträge zur Statistik 4, Universität Heidelberg 1993
[6] Dahlhaus R., Stoch. Proc. Appl. (1995)
[7] DOI: 10.2307/1425830 · Zbl 0276.62078
[8] Findley D., Beyond Chi-Square: Likelihood Ratio Procedures for Comparing Non-Nested, Possibly Incorrect Regressors (1989)
[9] Graybill F. A., Matrices with Application in Statistics, 2. ed. (1983) · Zbl 0496.15002
[10] Harvey A. C., Forecasting, structural time series models and the Kalman filter (1989)
[11] Millar P. W., Ecole d Eté de Probabilités de Saint-Flour XI-1981 976 (1983)
[12] Priestley M. B., J Roy Statist. Soc. Ser. 27 pp 204– (1965)
[13] Priestley M. B., Spectral Analysis and Time Series 2 (1981) · Zbl 0537.62075
[14] DOI: 10.1515/9783110850826 · Zbl 0594.62017
[15] DOI: 10.1017/S1446788700024137 · Zbl 0124.10504
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.