An exponential model for the spectrum of a scalar time series

Abstract

SUMMARY Existing procedures for obtaining linear prediction formulae for time series may be placed in two categories. The first consists of methods which involve fitting parametric models of the autoregressive or autoregressive moving average type. The second involves the factorization of an estimated spectral density function; this is essentially a nonparametric procedure. The procedure suggested in this paper contains elements of both of the above. Formally, it involves fitting a model with a finite number of parameters. However, the model is formulated explicitly in terms of the spectral density function, and may also be viewed as a spectrum factorization method. The model has been fitted to various series considered by other authors, and the quality of the fit is compared with that obtained with conventional models using the same number of parameters. Asymptotie properties of the parameter estimates have been used to assess the nonparametric spectrum factorization techniques proposed by other authors.