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

*(English)*Zbl 0822.62080Summary: 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.

##### MSC:

62M20 | Inference from stochastic processes and prediction |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

##### Keywords:

non-Gaussian filter; Gaussian mixture; outliers; Gaussian-sum smoother; two filter formula; non-Gaussian state space modeling; times series; non- Gaussian smoother; seasonal adjustment of economic time series
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\textit{G. Kitagawa}, Ann. Inst. Stat. Math. 46, No. 4, 605--623 (1994; Zbl 0822.62080)

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##### References:

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