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Seminar on Probability and Statistics
Seminar information archive ～04/17｜Next seminar｜Future seminars 04/18～
| Organizer(s) | Nakahiro Yoshida, Teppei Ogihara, Yuta Koike |
|---|
2007/06/27
16:20-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)
小方 浩明 (早稲田大学, 国際教養学部)
Empirical likelihood method for time series analysis
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/02.html
小方 浩明 (早稲田大学, 国際教養学部)
Empirical likelihood method for time series analysis
[ Abstract ]
For a class of vector-valued non-Gaussian stationary processes with unkown parameters, we develop the empirical likelihood approach which was proposed in the i.i.d. setting. In the time series analysis it is known that Whittle likelihood is one of fundamental tools to get a good estimator of unknown parameters and that the score functions are asymptotically normal. Motivated by the Whittle likelihood, we take its score as an estimating function and obtain the asymptotic distribution of our test statistic. Since the fitted spectral model may be different from true spectral structure, the results enable us to construct confidence rigions for various important time series parameters without knowing true spectral structure. We also consider the approach to a minimum contrast estimation and Cressie-Read power-divergence statistic. Numerical studies are introduced and illuminate some interesting features of the empirical approach.
[ Reference URL ]For a class of vector-valued non-Gaussian stationary processes with unkown parameters, we develop the empirical likelihood approach which was proposed in the i.i.d. setting. In the time series analysis it is known that Whittle likelihood is one of fundamental tools to get a good estimator of unknown parameters and that the score functions are asymptotically normal. Motivated by the Whittle likelihood, we take its score as an estimating function and obtain the asymptotic distribution of our test statistic. Since the fitted spectral model may be different from true spectral structure, the results enable us to construct confidence rigions for various important time series parameters without knowing true spectral structure. We also consider the approach to a minimum contrast estimation and Cressie-Read power-divergence statistic. Numerical studies are introduced and illuminate some interesting features of the empirical approach.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/02.html
