A periodic Levinson–Durbin algorithm for entropy maximization

Abstract

A recursive algorithm is presented for the computation of the first-order and second-order derivatives of the entropy of a periodic autoregressive process with respect to the autocovariances. It is an extension of the periodic Levinson–Durbin algorithm. The algorithm has been developed for use at one of the steps of an entropy maximization method developed by the authors. Numerical examples of entropy maximization by that method are given. An implementation of the algorithm is available as an R package.