Abstract The spectral estimation problem for a discrete-time series generated by a linear, time-invariant process can be formulated in terms of three models: autoregressive (AR), moving average (MA), and autoregressive-moving average (ARMA). Analysis procedures differ in each case, and specification errors arise due to application of the inappropriate algorithm. The AR and MA models lead respectively to the maximum entropy (MEM) and classical lag-window approaches. The ARMA model has much seismic interest because the unit impulse response of a horizontally stratified medium is expressible in this way. Since its feedback component has the minimum-delay property, an ARMA spectral estimation technique satisfying this requirement has particular seismic relevance. Such a spectral estimate results from the application of an iterative least-squares algorithm to selected gates of the observed time series. A sample set of synthetic time series serve to illustrate the degradation in the spectral estimate resulting from an incorrect specification of the model.