Seasonality and neural networks: a new approach
by Bruce Curry, Peter H. Morgan
International Journal of Metaheuristics (IJMHEUR), Vol. 1, No. 2, 2010

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.

Online publication date: Mon, 19-Jul-2010

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