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Predicting chaotic time series
Abstract
We present a forecasting technique for chaotic data. After embedding a time series in a state space using delay coordinates, we ``learn'' the induced nonlinear mapping using local approximation. This allows us to make short-term predictions of the future behavior of a time series, using information based only on past values. We present an error estimate for this technique, and demonstrate its effectiveness 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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Citations
Cited by
Sauer, T., Yorke, J. A., & Casdagli, M. (1991) · Journal of Statistical Physics · doi:10.1007/bf01053745 · Cited by 2,045
Physiological time-series analysis: what does regularity quantify?
Pincus, S. M., & Goldberger, A. L. (1994) · American Journal of Physiology-Heart and Circulatory Physiology · doi:10.1152/ajpheart.1994.266.4.h1643 · Cited by 1,315
A new evolutionary system for evolving artificial neural networks
Yao, X., & Liu, Y. (1997) · IEEE Transactions on Neural Networks · doi:10.1109/72.572107 · Cited by 874
Horizontal visibility graphs: Exact results for random time series
Luque, B., Lacasa, L., Ballesteros, F., & Luque, J. (2009) · Physical Review E · doi:10.1103/physreve.80.046103 · Cited by 789
Evolving fuzzy neural networks for supervised/unsupervised online knowledge-based learning
Kasabov, N. (2001) · IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) · doi:10.1109/3477.969494 · Cited by 482
Metadata
- Authors
- Farmer, J. D., & Sidorowich, J. J.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1987-08-24
- Volume
- 59
- Issue
- 8
- Pages
- 845-848
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2034099719
- Cited by
- 1,929
- References
- 0
- FWCI
- 19.64
- Type
- journal article
- Language
- en
- Open access
- closed
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- Farmer, J. D., & Sidorowich, J. J. (1987). Predicting chaotic time series. Physical Review Letters. https://doi.org/10.1103/physrevlett.59.845
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