Testing for time series linearity

In this paper, we present a procedure for testing the null hypothesis of linearity in a time series against the alternative of non‐linearity. Adapting the robust Wald‐type testing methods of Vogelsang (1998Econometrica66, 123–48), we provide a test statistic that has the same limiting null critical values regardless of whether the series under consideration is generated from a linear I(0) or linear I(1) process, and is consistent against non‐linearity of either form. Finite sample simulation evidence, together with empirical evidence from an application to US Dollar real exchange rates, suggests that our procedure should work well in practice.