Selection of weak VARMA models by Akaïke's information criteria

Yacouba Boubacar Mainassara (1)

1 EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie

This article considers the problem of orders selections of vector autoregressive moving-average (VARMA) models and the sub-class of vector autoregressive (VAR) models under the assumption that the errors are uncorrelated but not necessarily independent. We relax the standard independence assumption to extend the range of application of the VARMA models, and allow to cover linear representations of general nonlinear processes. We propose a modified criterion to the corrected AIC (Akaïke information criterion) version (AICc) introduced by Tsai and Hurvich (1989). This modified criterion is an approximately unbiased estimator of the Kullback-Leibler discrepancy, originally used to derive AIC-based criteria. Moreover, this criterion requires the estimation of the matrice involved in the asymptotic variance of the quasi-maximum likelihood (QML) estimator of the models, which provide an additional information about models. Monte carlo experiments show that the proposed modified criterion estimates the models orders more accurately than the standard AIC and AICc in large samples and often in small samples.

Mots clés: AIC; discrepancy; Kullback-Leibler information; QMLE/LSE; order selection; structural representation; weak VARMA models.; weak VARMA models

Domaines: Applications [stat.AP]

Yacouba Boubacar Mainassara. Selection of weak VARMA models by Akaïke's information criteria. 2010. ⟨hal-00493855v1⟩