ARMA spectral estimation based on partial autocorrelations

This paper presents a new method for estimating the coefficients of autoregressive moving-average parameters of stationary time series. The method is based on computing the sample autocorrelations of the given time series and fitting an ARMA model so as to approximate the partial autocorrelations in a least-squares sense. When the given time series are characterized by spectral zeroes near the unit circle, they tend to have relatively long sequences of nonzero partial autocorrelations; hence the new method is especially effective in such cases. This paper contains a derivation of all necessary mathematical details, as well as several numerical examples illustrating the performance.