In this paper we investigate the multi-period forecast performance of a number of empirical self-exciting threshold autoregressive (SETAR) models that have been proposed in the literature for modelling exchange rates and GNP, among other variables. We take each of the empirical SETAR models in turn as the DGP to ensure that the non-linearity characterizes the future, and compare the forecast performance of SETAR and linear autoregressive models on a number of quantitative and qualitative criteria. Our results indicate that non-linear models have an edge in certain states of nature but not in others, and that this can be highlighted by evaluating forecasts conditional upon the regime.
