Int. J. Metaheuristics, Vol. 1, No. 2, 2010 181 Copyright © 2010 Inderscience Enterprises Ltd. Seasonality and neural networks: a new approach Bruce Curry* and Peter H. Morgan Cardiff Business School, Cardiff University, Aberconway Building, Colum Drive, Cardiff CF10 3EU, UK Fax: 44-29-20874419 E-mail: curry@cardiff.ac.uk E-mail: MorganPH@cardiff.ac.uk *Corresponding author Abstract: This paper is a response to difficulties reported in applying feedforward neural networks (NNs) to seasonal data. The solution we propose is a modified network model which is pruned and optimised by means of Differential Evolution methods. The problem for NNs in the case of seasonality lies in the so-called ‘universal approximation’ property, which underpins the use of MLP networks as a vehicle for flexible non-linear regression. Our view is that seasonality is best modelled by using sinusoids, which permit the use of more powerful analytical tools without losing any generality as compared with dummy variables. However, the actual theorems supporting NN approximation specifically relate to functions possessing suitable properties of smoothness, in which case it is not surprising that NNs have difficulty with seasonality. Only a very ‘short’ sinusoid would be smooth enough. Our suggested solution is to transform the input variable so that instead of using a time variable alone we have sinusoids as inputs. In theoretical terms, this helps restore the approximation property, as can also be seen in our examples, which also serve to illustrate the strength of Differential Evolution methods. Keywords: neural network; NN; universal approximation; seasonality; Fourier series; evolutionary computation. Reference to this paper should be made as follows: Curry, B. and Morgan, P.H. (2010) ‘Seasonality and neural networks: a new approach’, Int. J. Metaheuristics, Vol. 1, No. 2, pp.181–197. Biographical notes: Bruce Curry is Emeritus Professor of Business Statistics at Cardiff Business School, Cardiff University, UK. His research interests incorporate business-related aspects of mathematics, statistics and computing. He has published many papers in important international journals on topics such as neural networks and rough sets. His work includes both theoretical aspects and applications of these topics. He has also acted as a Reviewer for a wide range of academic journals, across a variety of academic disciplines. Peter Morgan is currently a Reader in Quantitative Analysis at Cardiff Business School, Cardiff University, UK. Having been at Cardiff University since 1975 he joined the Business School in 1990 and teaches quantitative methods both to undergraduates and postgraduates. He holds a BSc (Tech.) in Industrial Chemistry and PhD in Polymer Physical Chemistry and has a background in chemical computing. He has also worked in the fields of technology transfer and innovation skills training. His research interests lie in the fields of neural networks, evolutionary programming and exploratory data analysis. He is also a member of the Violence and Society Research Group at Cardiff University.