The two-filter formula for smoothing and an implementation of the Gaussian-sum smoother
- 288 Downloads
A Gaussian-sum smoother is developed based on the two filter formula for smoothing. This facilitates the application of non-Gaussian state space modeling to diverse problems in time series analysis. It is especially useful when a higher order state vector is required and the application of the non-Gaussian smoother based on direct numerical computation is impractical. In particular, applications to the non-Gaussian seasonal adjustment of economic time series and to the modeling of seasonal time series with several outliers are shown.
Key words and phrasesNon-Gaussian smoother non-Gaussian filter Gaussian mixture nonstationary time series outliers seasonal adjustment
Unable to display preview. Download preview PDF.
- Alspach, D. L. and Sorenson, H. W. (1972). Nonlinear Bayesian estimation using Gaussian sum approximations,IEEE Trans. Automat. Control,AC-17, 439–448.Google Scholar
- Anderson, B. D. O. and Moore, J. B. (1979).Optimal Filtering, Prentice-Hall, New Jersey.Google Scholar
- Harrison, P. J. and Stevens, C. F. (1976). Bayesian forecasting (with discussion),J. Roy. Statist. Soc. Ser. B,34, 1–41.Google Scholar
- Kitagawa, G. (1987). Non-Gaussian state space modeling of nonstationary time series (with discussion),J. Amer. Statist. Assoc.,76, 1032–1064.Google Scholar
- Kitagawa, G. (1988). Numerical approach to non-Gaussian smoothing and its applications,Computing Science and Statistics: Proceedings of the 20th Symposium on the Interface (eds. E. J. Wegman, D. T. Gantz and J. J. Miller), 379–388.Google Scholar
- Kitagawa, G. (1989). Non-Gaussian seasonal adjustment,Comput. Math. Appl.,18(6/7), 503–514.Google Scholar
- Kitagawa, G. and Gersch, W. (1984). A smoothness priors-state space approach to the modeling of time series with trend and seasonality,J. Amer. Statist. Assoc.,79, 378–389.Google Scholar
- Sorenson, H. W. and Alspach, D. L. (1971). Recursive Bayesian estimation using Gaussian sums,Automatica,7, 465–479.Google Scholar
- Tsay, R. (1986). Time series modeling in the presence of outliers,J. Amer. Statist. Assoc.,81, 132–141.Google Scholar
- West, M. and Harrison, J. (1989). Bayesian forecasting and dynamic models, Springer Series in statistics, Springer, New York.Google Scholar