Autoregressive Moving Average Spectral Estimation: A Model Equation Error Procedure

A procedure is presented for generating an autoregressive moving average (ARMA) spectral model of a stationary time series based upon a finite set of time series' observations. The ARMA model's autoregressive coefficients are estimated by minimizing a quadratic function of a set of basic error terms. In examples treated to date, this method has demonstrated an exceptional ability in resolving closely spaced narrow band signals in a low signal-to-noise environment where other procedures such as the maximum entropy method often fail. Its effectiveness on other classes of time series also shows promise and a more general evaluation is presently being conducted. With this in mind, the new ARMA procedure promises to be an important spectral estimation tool.