  In this paper we derive the asymptotic distribution of normalized residual
empirical autocovariances and autocorrelations under weak assumptions on the
noise. We propose new portmanteau statistics for vector autoregressive
moving-average (VARMA) models with uncorrelated but non-independent innovations
by using a self-normalization approach. We establish the asymptotic
distribution of the proposed statistics. This asymptotic distribution is quite
different from the usual chi-squared approximation used under the independent
and identically distributed assumption on the noise, or the weighted sum of
independent chi-squared random variables obtained under nonindependent
innovations. A set of Monte Carlo experiments and an application to the daily
returns of the CAC40 is presented.
