A consistent nonparametric test for linearity of AR(p) models

We propose a simple nonparametric test for a linear AR(p) model against a general nonparametric AR(p) alternative. The asymptotic distribution of the test statistic under the null hypothesis of linearity is shown to be the standard normal. In addition, we show that the test is consistent against nonparametric AR(p) alternatives. © 1997 Elsevier Science S.A.