The Arov–Grossman Model and the Burg Multivariate Entropy

Abstract

In this article we deal with the Arov–Grossman functional model to describe all the solutions of the Covariance Extension Problem for q-variate stationary stochastic processes and we find the density that maximizes the Burg Multivariate Entropy. This description is based on a one-to-one correspondence between the set of all solutions of the Covariance Extension Problem and the set of all contractive analytic functions H from the open unit disk with values on the space of q × q matrices. With this correspondence, the density that maximizes the Burg Multivariate Entropy corresponds to the function H\equiv0. Also, from the information that the Arov–Grossman functional model provides we obtain a version of the Levinson algorithm. The partial autocorrelation coefficient matrices are computed directly from Levinson’s recursions.