Forecasting With Nonlinear Time Series Models

Abstract

Abstract This article considers nonlinear forecasting models, such as switching-regime models. These models are typically “small” compared to vector autoregressive and factor models, being either univariate or single-equation models, but tend to nest a linear relationship and so invite an assessment of whether allowing for nonlinearity improves forecast accuracy. The article is organized as follows. Section 2 considers a number of parametric time series models. Some universal approximators, including neural network models, are studied in Section 3. Forecasting several periods ahead with nonlinear models is the topic of Section 4. Forecasting with chaotic systems is briefly considered in Section 5. Comparisons of linear and nonlinear forecasts of economic time series are discussed in Section 6, and studies comprising a large number of series are discussed in Section 7. Section 8 contains a limited forecast accuracy comparison between recursive and direct forecasts. Final remarks and suggestions for further reading can be found in Section 9.