Statistical efficiency of the sample autocorrelation function in ARMA parameter estimation

Many modern ARMA spectral estimators are based either on the raw data or on some version of the lagged-product sample autocorrelation function (ACF). These two classes are compared in terms of their Cramer-Rao bound generalized variances in estimating the poles and zeros of the ARMA system generating the process. It is seen that the choice of lags of the sample ACF required to preserve most of the information in the data is signal dependent. Recommendations of a "good" information-preserving choice of lags for an AR(2) process in white noise are tabulated against pole magnitude and SNR. The case of two additive narrowband AR(2) processes is also studied.