Proof of Local Convergence of a New Algorithm for Covariance Matching of Periodic ARMA Models

Abstract

In a companion paper, the authors have proposed a new algorithm for the partial stochastic realization of vector discrete-time processes from finite covariance data, based on a nonlinear generalization of the classical Yule-Walker equations. In particular the algorithm provides solutions of the covariance matching problem for periodic ARMA models on a finite interval. In this letter, we provide a proof of convergence of the algorithm for scalar periodic ARMA models based on Lyapunov stability theory.