A Nonparametric Distribution-Free Test for Serial Independence of Errors

In this article, we propose a test for the serial independence of unobservable errors in location-scale models. We consider a Hoeffding–Blum–Kiefer–Rosenblat type empirical process applied to residuals, and show that under certain conditions it converges weakly to the same limit as the process based on true errors. We then consider a generalized spectral test applied to estimated residuals, and get a test that is asymptotically distribution-free and powerful against any type of pairwise dependence at all lags. Some Monte Carlo simulations validate our theoretical findings.