Predicting chaotic time series

Details Predicting chaotic time series Predicting chaotic time series

Aug 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987phrvl..59..845f&link_type=abstract

Physical Review Letters (ISSN 0031-9007), vol. 59, Aug. 24, 1987, p. 845-848.

Physics

377

Chaos, Prediction Analysis Techniques, Time Series Analysis, Couette Flow, Differential Equations, Errors, Random Processes, Rayleigh-Benard Convection

Scientific paper

A forecasting technique for chaotic data is presented. After a time series has been embedded in a state space using delay coordinates, the induced nonlinear mapping is 'learned' using a local approximation. This makes it possible to make short-term predictions of the future behavior of a time series, using information based only on past values. An error estimate is presented for this technique, and its effectiveness is demonstrated by applying it to several examples, including data from the Mackey-Glass delay differential equation, Rayleigh-Benard convection, and Taylor-Couette flow.

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