Auto-Regressive Moving Average Spectral Estimation Using Modified and Least Squares Modified Yule-Walker Estimates

摘要

Many popular contemporary spectral estimation methods invoke the modeling of the observation time series by a rational transfer function. These techniques employ the approximation of the second-order statistical relationships using the commonly known Yule-Walker equations. Solving these equations, one obtains the parameter estimates of the hypothesized rational transfer function model. These parameter estimates represent a set of autocorrelation time lags of the observation times series and are ideally selected to optimize the model being considered. Because of the optimization criteria, there are numerous methods/techniques which estimate parameters that have been proposed in the literature. The objective of this paper is to investigate two of these methods and report their respective performance. The most general rational transfer function containing both poles and zeros. Of the numerous techniques available in estimating the ARMA parameters, there are two which utilize the Modified Yule-Walker equations. This paper investigates both the Modified Yule-Walker (MYW) and Least Squares Modified Yule-Walter (LSMYW) methods in estimating an ARMA process. The MYW method estimates the ARMA parameters using a minimal set of Yule-Walker equations. In contrast, the LSMYW method utilizes the parametric estimation of an overdetermined set of Yule-Walker equations. (Author)