Time series prediction by adaptive networks: a dynamical systems perspective

The links between adaptive layered networks, functional interpolation and dynamical systems are considered and applied to the nonlinear predictive analysis of time series. The ability of networks to produce interpolation surfaces to generators of data (i.e. differential equations, iterative maps) is used to analyse a variety of time series. If a network may be trained to approximate a (static) generator of data, the network may be iterated on its own output to produce a time series with the same characteristics as the training waveform. However, since iterated networks are one example of nonlinear dynamical systems, this raises problems of sensitive dependence upon initial conditions leading ultimately to deterministic chaos. An introduction to the relevant concepts is presented and illustrations are provided from simple chaotic maps, nonlinear differential equations, and stock-market prediction. The latter example is included to illustrate the problems which often occur in real-world data due to noise, undersampling, high dimensionality and insufficient data