Tracking analysis of an ARMA parameter estimation algorithm using weak convergence theory

Abstract

In this paper we study the problem of adaptively estimating the Autoregressive Moving Average (ARMA) parameters of a time varying ARMA process using a constant step size Gauss-Newton Algorithm. Using weak convergence theory and the concept of prescaling, it is shown that the "mean" behavior can be described by an ordinary differential equation (ODE). Computer simulations are provided to substantiate the analysis.