Towards long-term prediction

This paper describes a simple method of obtaining longer-term predictions from a nonlinear time-series, assuming one already has a reasonably good short-term predictor. The usefulness of the technique is that it eliminates, to some extent, the systematic errors of the iterated short-term predictor. The technique we describe also provides an indication of the prediction horizon. We consider systems with both observational and dynamic noise and analyse a number of artificial and experimental systems obtaining consistent results. We also compare this method of longer-term prediction with ensemble prediction.