Uniqueness of a two-step predictor based spectral estimator that generalizes the maximum entropy concept

Given a finite set of autocorrelations, it is well known that maximization of the entropy functional subject to this data leads to a stable autoregressive model. Since maximization of the entropy functional is equivalent to maximization of the minimum mean square error associated with one-step predictors, the problem of obtaining admissible extensions that maximize the k-step minimum-mean-square prediction error subject to the given autocorrelations has been shown to result in stable autoregressive moving-average (ARMA) extensions. The uniqueness of this true generalization of the maximum-entropy extension is proved here by a constructive procedure in the case of two-step predictors