The paper considers bounds on the statistical efficiency of the estimators of the poles and zeros of an ARMA process based on estimates of the process autocorrelation function. Special attention is paid to autoregressive and autoregressive plus white noise processes. A measure of the statistical variability of the estimates is introduced as the ratio of the Cramer-Rao bounds on the generalised variances of estimates based on the unreduced data and on the autocorrelation function. Numerical values of this measure are presented for several processes of interest. Estimator performance is then related to pole-zero locations and the signal/noise ratio.