A well known result of Burg (1967) and Kunsch (1981) identifies a Gaussian Markov random field with autocovariances specified on a finite part L of the n-dimensional integer lattice, as the random field with maximum entropy among all random fields with same autocovariance values on L. A simple information theoretic proof of a version of the maximum entropy theorem for random fields in n dimensions is presented in the special case that the given autocovariances are compatible with a unilateral autoregressive process.

The standard maximum entropy method developed by J.P. Burg (1967) and the resulting autoregressive model have been widely applied to spectrum estimation and prediction. A generalization of the maximum entropy formalism in a nonparametric setting is presented, and the class of the resulting solutions is identified to be a class of Markov processes. The proof is based on a string of information theoretic arguments developed in a derivation of Burg's maximum entropy spectrum by B.S. Choi and T.M. Cover (1984). A framework for the practical implementation of the proposed method is presented in the context of both continuous and discrete data.>

A characterization of the stochastic process that has maximum entropy among all moving average processes of order q, subject to the condition that the autocovariances gamma (k) satisfy gamma (k)=c/sub k/, for k=0,1,. . ., p, is provided by exploiting properties of the inverse autocovariance sequence.>