We consider autoregressive models with moving average residuals (ARMA) and as special cases the autoregressive model (AR) and the moving average (MA). After a listing of properties of estimations of the parameters in these models we discuss an approximative likelihood ratio λ^* which was investigated by T.W. Anderson. We determine the asymptotic distribution of λ^* and with these results we get test for the orders of the autoregressive resp. the moving average part. In. the last section we consider the classifi-kation of a time series in one of two classes which are described by ARMA-models.