Generating prediction bands for path forecasts from SETAR models

Prediction bands for time series are usually generated point-wise by bootstrap methods. Such bands only convey the prediction uncertainty for each horizon separately. The joint distribution is not taken into account. To represent the forecast uncertainty over the entire horizon, methods for constructing joint prediction bands for path forecasts from SETAR models are proposed. This class of nonlinear models is increasingly used in time series analysis and forecasting as it is useful for capturing nonlinear dynamics. Approaches based on statistical theory and explicit sequential and global optimization methods are both considered. Monte Carlo simulation is used to assess the performance of the proposed methods. The comparison is done with regard to the actual coverage of the constructed prediction bands for full path forecasts as well as with regard to the width of the bands. An empirical application demonstrates the relevance of the choice of bands for indicating the uncertainty of path forecasts in nonlinear models.