A Monte Carlo Study of the Forecasting Performance of Empirical Setar Models

SUMMARY
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. Copyright C 1999 John Wiley & Sons, Ltd.
1. INTRODUCTION
In recent years there has been considerable interest in testing for and modelling non-linearities
in economic time series. Some of this activity has been based on allowing for non-linearities
in traditional econometric equations variously described as 'structural' or 'behavioural', but
much of it follows in the time-series tradition of Box and Jenkins (1970). The usefulness of linear
time-series models is usually gauged by their predictive ability, and such models have sometimes
been used as a benchmark for econometric models in forecast comparison. However, in a recent
review of non-linear time series models, De Gooijer and Kumar (1992) report that there is no
clear evidence in favour of non-linear over linear models in terms of forecast performance.
notwithstanding the ability of the former to capture asymmetries in important macro-aggregates
over the business cycle (see e.g. Hamilton, 1989; Tiao and Tsay, 1994; Potter, 1995 for US GNP,
Montgomery et al., 1997 for US unemployment, and Acemoglu and Scott, 1994 for UK labour
market variables).