For the stationary univariate ARMA-model hypotheses about the orders of the autoregressive and moving average parts are tested, based on a finite sequence of observations. It is done using the statistic where   respectively   are asymptotically efficient estimates of the error variances under the hypothesis respectively the alternative. It is shown that the statistic   is asymptotically equivalent to the likelihood ratio. The asymptotic distribution is central x²under the hypothesis and noncentral ξ²under a sequence of local alternatives.