On the use of autoregressive order determination criteria in multivariate white noise tests

Testing the hypothesis of multivariate white noise is seen as the selection of the order of a multivariate autoregressive model for the observed time series. Therefore, multivariate white noise tests can be carried out by applying autoregressive order-determination criteria such as AIC, BIC, etc. It is known, for example, that the BIC criterion estimates consistently the order of an autoregression. An order-determination criterion with this property leads to a white noise test with a significance level approaching zero as n, the number of observations, increases. The order of an autoregressive moving-average model is proposed to be determined by applying this kind of white noise test. The resulting model building procedure is a generalization of the procedure proposed by G.E.P. Box and G.M. Jenkins (1970)