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THE TWO-FILTER FORMULA FOR SMOOTHING AND

AN IMPLEMENTATION OF THE GAUSSIAN-SUM SMOOTHER

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GENSHIRO KITAGAWA

*The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, Japan*
(Received January 4, 1993; revised February 4, 1994)

**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.

**Source**
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