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.
We discuss the current state-of-the-art in non-linear modelling and forecasting, with particular emphasis placed on outlining a number of open issues. The topics we focus on include joint and conditional predictive density evaluation, loss functions, estimation and specification, and data-mining, amongst others. As such, this paper complements the rest of the papers in this special issue of the International Journal of Forecasting.
The rest of the paper is organized as follows. In Section 2 we discuss why one might want to consider non-linear models, and a number of reasons why their forecasting ability relative to linear models may not be as good as expected. In Section 3 we discuss recent theoretical and methodological issues to do with forecasting with non-linear models, many of which go beyond the traditional preoccupation with point forecasts to consider the whole predictive density. Section 4 highlights a number of empirical issues, and how these are dealt with in the papers collected in this issue. Concluding remarks are gathered in Section 5.
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