Application of Higher-Order Neural Networks to Financial Time-Series Prediction

Financial time series data is characterized by non-linearities, discontinuities and high frequency, multi-polynomial components. Not surprisingly, conventional Artificial Neural Networks (ANNs) have difficulty in modelling such complex data. A more appropriate approach is to apply Higher-Order ANNs, which are capable of extracting higher order polynomial coefficients in the data. Moreover, since there is a one-to-one correspondence between network weights and polynomial coefficients, HONNs (unlike ANNs generally) can be considered open-, rather than 'closed box' solutions, and thus hold more appeal to the financial community. After developing Polynomial and Trigonometric HONNs, we introduce the concept of HONN groups. The latter incorporate piecewise continuous activation functions and thresholds, and as a result are capable of modelling discontinuous (piecewise continuous) data, and what's more to any degree of accuracy. Several other PHONN variants are also described. The performance of P(T)HONNs and HONN groups on representative financial time series is described (credit ratings and exchange rates). In short, HONNs offer roughly twice the performance of MLP/BP on financial time series prediction, and HONN groups around 10% further improvement.