A three step algorithm for ARMA modeling

Abstract

A new ARMA estimation algorithm is proposed. It is based on a fundamental relationship which shows that the AR polynomial of an ARMA ( N, M) model belongs to the linear space spanned by the forward and backward linear predictors. This relationship allows us to construct an equivalent linear system with two inputs and the same output of the ARMA system. The inputs of this new system are the forward and backward linear prediction errors. As in this case the inputs and output are known, a least-squares identification algorithm is used to obtain the parameters of the system. These parameters define three polynomials. One of them is the AR polynomial. The other two converge asymptotically to the MA polynomial and to zero. Simple recursions are available to perform such a limiting operation.