(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.
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