The Spectral Analysis of Discrete Time Series in Terms Of Linear Regressive Models

摘要

The paper considers several methods for the spectral analysis of discrete time series modeled as linear regressive processes. The most general of these models is the so-called 'mixed-type' process in which the present value of the series is given a weighted sum of both its own past values and those of an uncorrelated random sequence. Special cases of this class are the autoregression and the moving average. In the present approach, the determination of the weighting coefficients of the model is equivalent to specifying the sampled power spectrum of the process, and the central problem treated here is that of estimating such a set of parameters on the basis of a sample sequence of the series. After a development of the necessary mathematical background, the estimation problem is formulated and solved from several alternative points of view, with particular attention to statistical stability, sample size requirements, and possible approximation errors. For each method, the results are demonstrated by a computational analysis of the spectra of a set of computer generated examples. A general purpose spectral analysis algorithm for digital computation is proposed and discussed. Methods for extending an existing spectral estimate to take into account newly available data are briefly explained, and suggestions for further research are presented. (Author)