A 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.