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FREQUENCY DOMAIN CHARACTERISTICS OF LINEAR

OPERATOR TO DECOMPOSE A TIME SERIES INTO

THE MULTI-COMPONENTS

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T. HIGUCHI

*The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, Japan*
(Received April 19, 1990; revised March 18, 1991)

**Abstract.**
Frequency domain properties of the operators to
decompose a
time series into the multi-components along the Akaike's Bayesian model
(Akaike
(1980, *Bayesian Statistics*, 143-165, University Press, Valencia,
Spain))
are shown. In that analysis a normal disturbance-linear-stochastic regression
prior model is applied to the time series.
A prior distribution, characterized by a small number of
hyperparameters, is specified for model parameters.
The posterior distribution is a linear function (filter) of observations.
Here we use frequency domain analysis or filter characteristics of several
prior models parametrically as a function of the hyperparameters.

*Key words and phrases*:
Time series, Bayesian approach,
signal decomposition, linear filter, variable kernel, curve smoothing,
smoothness prior, seasonal component model, quasi-sinusoidal wave
extraction.

**Source**
( TeX ,
DVI ,
PS )