Application of the multi-model partitioning theory for simultaneous order and parameter estimation of multivariate ARMA models

In this paper, a study on how to perform simultaneous order and parameter estimation of multivariate (MV) ARMA (autoregressive moving average) models under the presence of noise is addressed. The proposed method, which is computationally efficient, is an extension of a previously presented method for MV AR models and is based on the well established and widely applied multi-model partitioning theory. A series of computer simulations indicate that the method is infallible in selecting the correct model order in very few steps. The simultaneous estimation of the multivariate ARMA parameters is also another benefit of the proposed method. The results are compared with two other established order selection criteria namely Akaike's Information Criterion (AIC) and Schwarz's Bayesian Information Criterion (BIC). Finally, it is shown that the method is also successful in tracking model order changes, in real time.