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 ( 1998 Econometrica 66, 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.