Convergence analysis of ladder algorithms for AR and ARMA models

Abstract

A class of exact fast algorithms originally introduced in the signal processing area is provided by the so-called recursive least squares ladder forms. The many nice numerical and structural properties of these algorithms have made them a very powerful alternative in a very large variety of applications. Yet the convergence properties of the algorithms have not received the necessary attention. This paper gives an asymptotic analysis of two particular ladder algorithms, designed for auto-regressive (AR) and auto-regressive-moving-average (ARMA) models. Convergence is studied based on the stability properties of an associated differential equation. The conditions obtained for the convergence of the algorithms parallel those known for prediction error methods and for a particular type of pseudo-linear regression.