Convergence analysis of ladder algorithms for AR and ARMA models

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 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 ladder algorithms, designed for autoregressive (AR) and autoregressive moving average (ARMA) models. Convergence is studied based on the stability properties of an associated differential equation. It is shown that the convergence conditions obtained for the algorithms parallel those known for prediction error methods and for a particular type of pseudo-linear regression. © 1986.