Forecasting with nonlinear time series models

In this paper, nonlinear models are restricted to mean nonlinear parametric models. Several such models popular in time series econometrics are presented and some of their properties discussed. This includes two models based on universal approximators: the Kolmogorov-Gabor polynomial model and two versions of a simple artificial neural network model. Techniques for generating multi-period forecasts from nonlinear models recursively are considered, and the direct (non-recursive) method for this purpose is mentioned as well. Forecasting with complex dynamic systems, albeit less frequently applied to economic forecasting problems, is briefly highlighted. A number of large published studies comparing macroeconomic forecasts obtained using different time series models are discussed, and the paper also contains a small simulation study comparing recursive and direct forecasts in a particular case where the data-generating process is a simple artificial neural network model. Suggestions for further reading conclude the paper.