Testing for nonlinearity in mean in the presence of heteroskedasticity

This paper considers an important practical problem in testing time-series data for nonlinearity in mean. Most popular tests reject the null hypothesis of linearity too frequently if the the data are heteroskedastic. Two approaches to redressing this size distortion are considered, both of which have been proposed previously in the literature although not in relation to this particular problem. These are the heteroskedasticityrobust-auxiliary-regression approach and the wild bootstrap. Simulation results indicate that both approaches are e¤ective in reducing the size distortion and that the wild bootstrap o¤ers better performance in smaller samples. Two practical examples are then used to illustrate the procedures and demonstrate the potential pitfalls encountered when using non-robust tests. Keywords nonlinearity in mean, heteroskedasticity, wild bootstrap, empirical size and power JEL Classi…cation C12, C22, C52 Corresponding author Ralf Becker