Time series, neural networks and the future of the Sun
Abstract
The prediction of time series is discussed in general, with particular attention given to the use of feed forward neural networks in predicting solarterrestrial time series. Firstly, a variety of methods of describing and predicting time series are reviewed, and in so doing are placed in mutual context. Feed forward neural networks, which have received so much attention in recent literature, are discussed in some detail, in terms of how they represent and learn to represent functional relationships. This is then related to their ability to predict time series. Other important types of neural network are also briefly discussed. As sunspot number has become the most popular test bed of many time series models, and because prediction of solar maximum is important for many reasons, its history is reviewed and the statistical properties of the solar cycle are analysed. In particular, no evidence for a mean cycle is found and a statistically significant change in the variation of cycle lengths is found to occur in the mid19th century. The implications of this latter result for prediction are discussed, bearing in mind the known unreliability of sunspot number reconstructed by R. Wolf. Some results on predicting sunspot number, 10.7 cm solar flux and K_{p} geomagnetic index are then presented. In particular the best networks for predicting these time series are identified, together with various details on the residuals of prediction. Variations on the standard use of neural networks are also discussed, including results from wavelet prediction, where the time series is decomposed into different timescales prior to prediction, and dual data input networks, where more than one time series is inputted to the network. Finally, several nonneural methods for predicting solarterrestrial time series are reviewed.
 Publication:

New Astronomy Reviews
 Pub Date:
 October 1998
 DOI:
 10.1016/S13876473(98)000414
 Bibcode:
 1998NewAR..42..343C