A Study of Autoregressive and Window Spectral Estimation

Abstract

SUMMARY a process with a mixed spectrum. The paper also includes some discussion of two different methods of estimating the coefficients of AR models (the Burg method and the Yule-Walker approach), and of the performance of various order determination criteria, such as FPE, AIC and CAT. 1. I NTRODUCTION The problem of fitting finite parameter linear models to time series has recently aroused renewed interest, particularly in relation to the use of automatic model order determination procedures such as Akaike's AIC and Parzen's CAT criteria. Such models can be used to provide parametric estimates of the spectral density function, and, in particular, the method of autoregressive spectral estimation has attracted growing interest as an alternative to the more traditional non-parametric methods. In this paper we compare the relative merits of AR and window spectral estimation, the basis of the work being an extensive simulation of series constructed from a variety of models. The simulation study also provides valuable information on the relative performance of various order determination criteria when applied to different types of models and varying data lengths. Our conclusions are summarized in Section 7.