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The two-filter formula for smoothing and an implementation of the Gaussian-sum smoother

  • Genshiro Kitagawa
Time Series Analysis

Abstract

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 phrases

Non-Gaussian smoother non-Gaussian filter Gaussian mixture nonstationary time series outliers seasonal adjustment 

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References

  1. 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
  2. Anderson, B. D. O. and Moore, J. B. (1979).Optimal Filtering, Prentice-Hall, New Jersey.Google Scholar
  3. Harrison, P. J. and Stevens, C. F. (1976). Bayesian forecasting (with discussion),J. Roy. Statist. Soc. Ser. B,34, 1–41.Google Scholar
  4. Kitagawa, G. (1987). Non-Gaussian state space modeling of nonstationary time series (with discussion),J. Amer. Statist. Assoc.,76, 1032–1064.Google Scholar
  5. 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
  6. Kitagawa, G. (1989). Non-Gaussian seasonal adjustment,Comput. Math. Appl.,18(6/7), 503–514.Google Scholar
  7. 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
  8. Sorenson, H. W. and Alspach, D. L. (1971). Recursive Bayesian estimation using Gaussian sums,Automatica,7, 465–479.Google Scholar
  9. Tsay, R. (1986). Time series modeling in the presence of outliers,J. Amer. Statist. Assoc.,81, 132–141.Google Scholar
  10. West, M. and Harrison, J. (1989). Bayesian forecasting and dynamic models, Springer Series in statistics, Springer, New York.Google Scholar

Copyright information

© The Institute of Statistical Mathematics 1994

Authors and Affiliations

  • Genshiro Kitagawa
    • 1
  1. 1.The Institute of Statistical MathematicsTokyoJapan

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