Whilst non-linear models are often used for a variety of purposes, one of their prime uses is for forecasting, and it is in terms of their forecasting performance that they are most often judged. However, a casual review of the literature suggests that often the forecasting performance of such models is not particularly good. Some studies find in favour, but equally there are studies in which their added complexity relative to rival linear models does not result in the expected gains in terms of forecast accuracy. Just over a decade ago, in their review of non-linear time series models, De Gooijer and Kumar (1992) concluded that there was no clear evidence in favour of non-linear over linear models in terms of forecast performance, and we suspect that the situation has not changed very much since then. It seems that we have not come very far in the area of non-linear forecast model construction.
We argue that the relatively poor forecasting performance of non-linear models calls for substantive further research in this area, given that one might feel uncomfortable asserting that non-linearities are unimportant in describing economic and financial phenomena. The problem may simply be that our non-linear models are not mimicing reality any better than simpler linear approximations, and in the next section we discuss this and related reasons why a good forecast performance ‘across the board’ may constitute something of a ‘holy grail’ for non-linear models.