TESTING FOR SERIAL-CORRELATION AGAINST AN ARMA(1,1) PROCESS

This article is concerned with tests for serial correlation in time se ries and in the errors of regression models. In particular, the nonsta ndard problem of testing for white noise against autoregressive moving average model ARMA(1, 1) alternatives is considered. The likelihood r atio (LR), sup Lagrange multiplier (LM), and exponential average LM an d LR tests are shown to be asymptotically admissible for ARMA(1, 1) al ternatives. In addition, they are shown to be consistent against all ( weakly stationary strong mixing) non-white noise alternatives. Simulat ion results compare the tests to several tests in the literature. Thes e results show that the LR and Exp-LR infinity tests have very good al l-around power properties for nonseasonal alternatives.