In this paper we investigate the multi-period forecast performance of a num
ber of empirical self-exciting threshold autoregressive (SETAR) models that
have been proposed in the literature for modelling exchange rates acid 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, an
d compare the forecast performance of SETAR and linear autoregressive model
s on a number of quantitative and qualitative criteria. Our results indicat
e that non-linear models have an edge in certain states of nature but not i
n others, and that this can be highlighted by evaluating forecasts conditio
nal upon the regime. Copyright (C) 1999 John Wiley & Sons, Ltd.