A test for randomness against ARMA alternatives

In a recent paper, Mokkadem (1997. Stoch. Proc. Appl. 72, 145–149) derived a simple test for randomness against ARMA alternatives. In this note we consider a transformation of the corresponding statistic and present an alternative proof of this result. Through this approach it is demonstrated that the asymptotic distribution of the corresponding test statistic under the alternative does not depend on the fourth-order moments of the innovations. A simulation study indicates that a transformation of the test of Mokkadem (1997) (which is asymptotically equivalent to the classical portmanteau test) may perform better for finite sample sizes.