FREQUENCY DOMAIN CHARACTERISTICS OF LINEAR OPERATOR TO DECOMPOSE A TIME SERIES INTO

THE MULTI-COMPONENTS

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.