Extraction of nonlinear dynamics from short and noisy time series

The aim of this paper is to define efficient strategies for the modeling an d predicting of short and noisy time series with neural networks. Several c omplementary methods are tested on short series constructed from the Lorenz system which has been spoiled with various levels of measurement or dynami cal noise. The best strategies are selected from the simulation results acc ording to the level and the noise characteristics. In the presence of measu rement noise we show that over-sizing of the embedding dimension of the lea rning set increases the powerness of neural network fits. In the case of dy namical noise spoiling, we found that generation of a new trajectory predic ted with local operators, amplifying information of the original series, al lows the usage of neural networks as in the case of measurement noise, and so, avoids over-fitting problems possible with very short series. The strat egies applied to the real biological and astronomical data (whooping cough in Great Britain and Wolf sunspot numbers) revealed their deterministic ske letons showing chaotic attractors. (C) 2001 Elsevier Science Ltd. All right s reserved.