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Some Practical Considerations of Predictability and Learning Algorithms for Various Signals In this chapter, predictability, detecting nonlinearity and performance with respect to the prediction horizon are considered. Methods for detecting nonlinearity of signals are first discussed. Then, different algorithms are compared for the prediction of nonlinear and nonstationary signals, such as real NO2 air pollutant and heart rate variability signals, together with a synthetic chaotic signal. | Recurrent Neural Networks for Prediction Authored by Danilo P. Mandic Jonathon A. Chambers Copyright 2001 John Wiley Sons Ltd ISBNs 0-471-49517-4 Hardback 0-470-84535-X Electronic 11 Some Practical Considerations of Predictability and Learning Algorithms for Various Signals Perspective In this chapter predictability detecting nonlinearity and performance with respect to the prediction horizon are considered. Methods for detecting nonlinearity of signals are first discussed. Then different algorithms are compared for the prediction of nonlinear and nonstationary signals such as real NO2 air pollutant and heart rate variability signals together with a synthetic chaotic signal. Finally bifurcations and attractors generated by a recurrent perceptron are analysed to demonstrate the ability of recurrent neural networks to model complex physical phenomena. Introduction When modelling a signal an initial linear analysis is first performed on the signal as linear models are relatively quick and easy to implement. The performance of these models can then determine whether more flexible nonlinear models are necessary to capture the underlying structure of the signal. One such standard model of linear time series the auto-regressive integrated moving average or ARIMA p d q model popularised by Box and Jenkins 1976 assumes that the time series xk is generated by a succession of random shocks ek drawn from a distribution with zero mean and variance a2. If xk is non-stationary then successive differencing of xk via the differencing operator xk xk xk-1 can provide a stationary process. A stationary process zk dxk can be modelled as an autoregressive moving average p q zk aizk-i I bi k-i k. Of particular interest are pure autoregressive AR models which have an easily understood relationship to the nonlinearity detection technique of DVS deterministic 172 INTRODUCTION Time scale in hours a The raw NO2 time series Figure The NO2 time series and its autocorrelation