Improved ARMA spectral estimation

Abstract

The autoregressive (AR) spectral estimator has been studied by several authors, Parzen [10], Burg [3], and Marple [7] to name but a few. Even though the results of Burg and later results of Nuttal [9], Ulrych and Clayton [14] and also Marple [7] significantly improved the AR spectral estimator, it still is somewhat disappointing for narrow band signals or for nearly noninvertible auroregressive moving average (ARMA) data. To circumvent the difficulties, while at the same time introducing a more robust estimator, several authors have suggested the use of the ARMA spectral estimator (e.g. Morton and Gray [8] and Cadzow [4]). In this paper, a new ARMA spectral estimator is introduced which, using a recent result of Tiao and Tsay [12], makes use of dynamic prefiltering. It seems to perform better than previously defined ARMA spectral estimators and the AR spectral estimators of Burg or Marple. Examples are given which include data which is ARMA and data which is not ARMA. Several references to work in this area are included.