| Paper title: |
Predicting Chaos |
| Published in: | Issue 2, (Vol. 6) / 2012 |
| Publishing date: | 2011-10-24 |
| Pages: | 79-82 |
| Author(s): | VLAD Sorin |
| Abstract. | The main advantage of detecting chaos is that the time series is short term predictable. The prediction accuracy decreases in time. A strong evidence of chaotic dynamics is the existence of a positive Lyapunov exponent (i.e. sensitivity to initial conditions). In chaotic time series prediction theory the methods used can be placed in two classes: global and local methods. Neural networks are global methods of prediction. The paper tries to find a relation between the two parameters used in reconstruction of the state space (embedding dimension m and delay time τ) and the number of input neurons of a multilayer perceptron (MLP). For two of three time series studied, the minimum absolute error value is minimum for a MLP with the number of inputs equal to m*τ. |
| Keywords: | Chaos Theory, Time Series, Chaos Identification, Prediction |
| References: | 1. Sugihara G., May M. Robert, “Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series”, Nature, vol, 334, No. 6268, 1990, pp.734- 741. 2. Deco G, Schurmann B., “Information Dynamics” Springer-Verlag, 2001. 3. Sprott J. C. “Chaos and time series analysis”, Oxford University Press, 2003 4. P. Grassberger, I. Procaccia. Measuring the strangeness of strange attractors, PhysicaD, 1983,(9):346. 5. Small M., “Applied Nonlinear Time Series Analysis. Applications in physics, physiology and finance”, World Scientific Publishing Co., 2005 6. Wolf A., “Determining Lyapunov exponents from a time series”, Physica, 16D, 1985 |
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