Search

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. [ABSTRACT FROM AUTHOR]

A generalized information criterion is proposed to determine an embedding dimension and a delay time for delay coordinates of the reconstructed dynamics both for linear stochastic and nonlinear deterministic processes. While the standard maximum likelihood type method requires statistical parametric models such as autoregressive models, the generalized information criterion is constructed from the quantity in accordance with the second-order Renyi entropy in terms of the correlation integral for the finite number of data which is directly obtained from a time delay vector. It is found numerically that the present method works well when applied to chaotic and stochastic systems. [ABSTRACT FROM AUTHOR]