A periodic Levinson–Durbin algorithm for entropy maximization

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.

► We consider maximum entropy estimation of periodically correlated time series.
► We give an algorithm for computation of the derivatives and the Hessian of the entropy.
► We extend the periodic Levinson–Durbin algorithm to the computation of derivatives.
► Numerical examples show the excellent properties of our maximum entropy method.
► The method is very reliable, even in the semi-definite case, and is useful in signal processing, for example.