Abstract This paper proposes a simple chartist-fundamentalist model in which we allow for nonlinear time variation in chartists’ extrapolation rate. Estimation of the model using monthly data for the major currencies vis-a-vis the US dollar shows that the model is significant in-sample and that it has out-of-sample predictive power for some of the currencies. We investigate the power of tests of the random walk model to detect predictability against the alternative of the proposed model. We find that the evidence of short-term unpredictability and the long-term predictability are consistent with our model.