Stochastically equivalent dynamical system approach to nonlinear deterministic prediction

We propose a new prediction method for nonlinear time series based on the paradigm of deterministic chaos. Introducing a stochastically equivalent dynamical system to an original map, a prediction method is derived by minimizing a random term that defines intervals in which a good prediction performance is obtained. The use of the present method is illustrated for some chaotic systems with particular emphasis on issues of choices of variable time steps that are necessary when discretizing the stochastic differential equation. Applying to some systems, it is found that the present method works better than traditional chaotic methods.