Forecasting chaos from small data sets: a comparison of different nonlinear algorithms

Abstract

We compare the capabilities of different nonlinear algorithms for forecasting chaotic time series when a limited number of past values of the series is available, a situation most often found in real-world problems. In particular, we consider instance-based methods and neural network techniques, which are frequently advocated in the literature as universal, simple, and fairly reliable algorithms for time-series analysis. Furthermore, we propose a linear correction to the instance-based Wimplex method that produces remarkably good results on clean data. Finally, we present a preliminary application of the ideas discussed here to the real-world series of solar activity, which is often taken as a benchmark for these kinds of studies.