Comparison of several methods to predict chaotic time series

The aim of this paper is to compare different prediction methods for chaotic deterministic systems. We consider three different methods to evaluate the dynamics of the systems: the nearest neighbors, the radial basis functions and the regression tree. We use a comparison criterion suited to chaotic systems: the prediction horizon. The optimal prediction horizon is discussed with respect to the sampling time step. We apply these methods to simulated chaotic systems (Lorenz systems), experimental chaotic systems (double-scroll) and to intra-day series of exchange rates, namely Deutschmark/French Franc. We provide developments concerning the choice of the parameters involved in chaotic time series prediction