Support Vector Echo-State Machine for Chaotic Time-Series Prediction

A novel chaotic time-series prediction method based on support vector machines (SVMs) and echo-state mechanisms is proposed. The basic idea is replacing "kernel trick" with "reservoir trick" in dealing with nonlinearity, that is, performing linear support vector regression (SVR) in the high-dimension "reservoir" state space, and the solution benefits from the advantages from structural risk minimization principle, and we call it support vector echo-state machines (SVESMs). SVESMs belong to a special kind of recurrent neural networks (RNNs) with convex objective function, and their solution is global, optimal, and unique. SVESMs are especially efficient in dealing with real life nonlinear time series, and its generalization ability and robustness are obtained by regularization operator and robust loss function. The method is tested on the benchmark prediction problem of Mackey-Glass time series and applied to some real life time series such as monthly sunspots time series and runoff time series of the Yellow River, and the prediction results are promising.

Approach to predictability via anticipated synchronization

Predictability of chaotic systems is limited, in addition to the precision of the knowledge of the initial conditions, by the error of the models used to extract the nonlinear dynamics from the time series. In this paper, we analyze the predictions obtained from the anticipated synchronization scheme using a chain of slave neural network approximate replicas of the master system. We compare the maximum prediction horizons obtained with those attainable using standard prediction techniques.