A new test for ARMA models with errors following a general white noise process

Summary The aim of this paper is to present a new test for ARMA models. The consistency of this sequence of tests is proved using the asymptotic separation of the two sequences of probability laws defined by each hypothesis to be tested. Furthermore, we illustrate the adequacy of this test for general ARMA models in which the error process is conditionally heteroscedastic white noise. Therefore, beyond its application to classical ARMA processes, this test is also well-adapted to ARMA-GARCH and ARMA-GTARCH models.