Estimating the orders of weak multivariate ARMA models

In this Note, we consider the problem of order selection of vector autoregressive moving-average (VARMA) models under the assumption that the errors are uncorrelated, but not necessarily independent. These models are called weak VARMA by opposition to the standard VARMA models, also called strong VARMA models, in which the error terms are supposed to be iid. This selection is based on minimizing an information criterion, especially that introduced by Akaike. The theoretical foundations of the Akaike information criterion (AIC) are not more established when the iid assumption on the noise is relaxed. We propose a modified AIC criterion, and which may be very different from the standard AIC criterion. (C) 2011 Academic des sciences. Publie par Elsevier Masson SAS. Tous droits reserves.