SUMMARYA new procedure is proposed for modelling nonlinearity of a smooth transition form, by allowing the transition variable to be a weighted function of lagged observations. This function depends on two unknown parameters and requires specification of the maximum lag only. Nonlinearity testing for this specification uses a search over a plausible set of weight function parameters, combined with bootstrap inference. Finite‐sample results show that the recommended wild bootstrap heteroskedasticity‐robust testing procedure performs well, for both homoskedastic and heteroskedastic data‐generating processes. Forecast comparisons relative to linear models and other nonlinear specifications of the smooth transition form confirm that the new WSTR model delivers good performance. Copyright © 2010 John Wiley & Sons, Ltd.