The multivariate portmanteau test proposed by Hosking (1980) for testing the adequacy of an autoregressive moving average model is based on the first s residual autocovariances of the fitted model.In practice a value for s is chosen in dependence on the sample size n, mostly s = 20 for n between 50 and 200. In this paper it will be shown by simulations that the usual choiceof s = 20 oftenleads to a significant deviation of the sample distribution of the test statistic Pmfrom the asymptotic X2distribution. In the case of pure multivariate AR models the Kolmogorow-Smirnow test is used to find those values of s for which the sample distribution shows the best agreement with X2.In this manner s depends not only on the sample size n but also on the order of themodel p and the dimension m. A table for the best choice of s is given for n between 100 and 1000,p between 1 and 5 and m between 1 and 12.