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 con sider a transformation of the corresponding statistic and present an altern ative proof of this result. Through this approach it is demonstrated that t he asymptotic distribution of the corresponding test statistic under the al ternative 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. (C) 2000 Elsevier Science B.V . All rights reserved.