Chaotic time series Part II: System identification and prediction

Details Chaotic time series Part II: System identification and prediction Chaotic time series Part II: System identification and prediction

1994-01-14

arxiv.org/abs/chao-dyn/9401003v2

Nonlinear Sciences

Chaotic Dynamics

17 pages and 3 pages with figures all in uuencoded tar-compressed postscript format. Sent to Modeling, Identification and Cont

Scientific paper

This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear methods. However, the deterministic structure may be uncovered and non-linear models constructed that allow improved prediction. We give the background for such methods from a geometrical point of view, and briefly describe the following types of methods: global polynomials, local polynomials, multi layer perceptrons and semi-local methods including radial basis functions. Some illustrative examples from known chaotic systems are presented, emphasising the increase in prediction error with time. We compare some of the algorithms with respect to prediction accuracy and storage requirements, and list applications of these methods to real data from widely different areas.

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