Spectral Estimation: Fact or Fiction

The spectral estimation problem for a discrete time series generated by a linear time-invariant process can be described in terms of three models: autoregressive (AR), moving average (MA), and autoregressive-moving average (ARMA). Application of a particular spectral estimator to an inappropriate model can result in serious errors. The AR and MA models lead, respectively, to the maximum entropy method (MEM) and classical lag-window approaches. For the ARMA model, we have developed an iterative least squares technique which has an important property, namely, that the feedback component of this response has the minimum delay property. Finally, we present a study to illustrate the degradation in performance resulting from application of the incorrect spectral estimation method to given synthetic data sets.