Abstract
Time series often exhibit periodical patterns that can be analysed by conventional statistical techniques. These techniques rely upon an appropriate choice of model parameters that are often difficult to determine. Whilst neural networks also require an appropriate parameter configuration, they offer a way in which non-linear patterns may be modelled. However, evidence from a limited number of experiments has been used to argue that periodical patterns cannot be modelled using such networks. Researchers have argued that combining models for forecasting gives better estimates than single time series models particularly for seasonal and cyclic series. For example, a hybrid architecture comprising an autoregressive integrated moving average model (ARIMA) and a neural network is a well-known technique that has recently been shown to give better forecasts by taking advantage of each model's capabilities. However, this assumption carries the danger of underestimating the relationship between the model's linear and non-linear components, particularly by assuming that individual forecasting techniques are appropriate, say, for modelling the residuals. In this thesis, we show that such combinations do not necessarily outperform individual forecasts. On the contrary, we show that the combined forecast can underperform significantly compared to its constituents'. We also present a method to overcome the perceived limitations of neural networks by determining the configuration parameters of a time delayed neural network from the seasonal data it is being used to model. The motivation of our method is that Occam's razor should guide us in selecting a simpler solution compared to a complex solution. Our method uses a fast Fourier transform to calculate the number of input tapped delays, with results demonstrating improved performance as compared to that of other linear and hybrid seasonal modelling techniques on twelve benchmark time series. Keywords: neural networks, time series, cycles, ARIMA-NN hybrids, Fourier, TDNN.