Order Estimation of Multivariate ARMA Models

Model order estimation is fundamental in the system identification process. In this paper, we generalize a previous multivariate autoregressive (AR) model order estimation method (J. Lardies and N. Larbi, A new method for model order selection and model parameter estimation in time domain, J. Sound Vibr., vol. 245, no. 2, 2001) to include multivariate autoregressive moving average (ARMA) models and propose a modified model order selection criterion. We discuss the performance analysis of the proposed criterion and show that it has a lower error probability for model order selection when compared to the criterion of G. Liang et al. ARMA model order estimation based on the eigenvalues of the covariance matrix, IEEE Trans. Signal Process., vol. 41, no. 10, pp. 3009-03009, Oct. 1993). A Monte-Carlo (MC) analysis of the model order selection performance under different noise variations and randomized model parameters is performed, allowing the MC results to be generalized across model parameter values and various noise levels. Finally we validate the model for both simulated data and real electroencephalographic (EEG) data by spectral fitting, using the model order selected by the proposed technique as compared to that selected by Akaike's Information Criterion (AIC). We demonstrate that with the proposed technique a better fit is obtained.