A new recursive pseudo least squares algorithm for ARMA filtering and modeling. I

Abstract

This study is based on the observation that if the bootstrapping is combined with different parameterizations of the ARMA (autoregressive moving average) process, then different linearized problems are obtained for the underlying nonlinear ARMA modeling problem. In this part, a specific parameterization termed the predictor space representation for an ARMA process, which decouples the estimation for the AR and the MA parameters, is used. A vector space formalism for the given data case is then defined, and the least-squares ARMA filtering problem is interpreted in terms of projection operations on some linear spaces. A new projection operator update formula, which is particularly suited for the underlying problem, is then used in conjunction with the vector space formalism to develop a computationally efficient pseudo-least-squares algorithm for ARMA filtering. It is noted that these recursions can be put in the form of a filter structure.