High performance spectral estimation--A new ARMA method

In this paper a method for generating an ARMA model spectral estimate of a wide-sense stationary time series from a finite set of observations is presented. The method is based upon a set of error equations which are dependent on the ARMA model´s parameters. Minimization of a quadratic functional of these error equations with respect to the ARMA model´s parameters produces the desired spectral estimate. In examples treated to date, this ARMA spectral estimator has provided significantly better performance when compared to such standard procedures as the maximum entropy and Box-Jenkins methods. The computational requirements of this new method basically entail the solving of a system of p linear equations in the autoregressive coefficients where p denotes the order of the ARMA model. Since an ARMA model will typically be of lower order than its autoregressive model counterpart for a specified fidelity of match, the new ARMA procedure is generally more efficient computationally than the maximum entropy method. With this in mind, this ARMA method offers the promise of being a primary tool in many spectral estimation applications.