Tests portmanteau multivariés d'adéquation de modèles VARMA faibles

Abstract

In this Note, we consider portmanteau tests for testing the adequacy of vector autoregressive moving-average (VARMA) 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, allowing us to treat linear representations of general nonlinear processes. We first study the joint distribution of the quasi-maximum likelihood estimator (QMLE) and the noise empirical autocovariances. We thus obtain the asymptotic distribution of residual empirical autocovariances and autocorrelations under weak assumptions on the noise. We deduce the asymptotic distribution of the Ljung–Box (or Box–Pierce) portmanteau statistics for VARMA models with nonindependent innovations. We propose a method to adjust the critical values of the portmanteau tests.