Selection of weak VARMA models by modified Akaike’s information criteria

This article considers the problem of order selection of the vector autoregressive moving-average models and of the sub-class of the vector autoregressive models under the assumption that the errors are uncorrelated but not necessarily independent. We propose a modified version of the AIC (Akaike information criterion). This criterion requires the estimation of the matrice involved in the asymptotic variance of the quasi-maximum likelihood estimator of these models. Monte carlo experiments show that the proposed modified criterion estimates the model orders more accurately than the standard AIC and AICc (corrected AIC) in large samples and often in small samples.