Evaluating non-linear models on point and interval forecasts: an application with exchange rate returns

The aim of this paper is to compare the forecasting performance of SETAR and GARCH models against a linear benchmark using historical data for the returns of the Japanese yen/US dollar exchange rate. The relative performance of the models is evaluated on point forecasts and on interval forecasts. Point forecasts evaluation over the whole forecast period indicates that the performance of the models, when distinguishable, tends to favour the linear models. However, we show that if the evaluation of point forecasts is conducted over distinct subsamples or specific regimes there is more evidence of forecasting gains, especially from the SETAR models. Moreover, when we evaluate the validity of interval forecasts, the results produce clear evidence of the superiority of the non-linear models, and tend to favour especially the GARCH models.