Financial time-series data is characterized by nonlinearities, discontinuities, and high-frequency multipolynomial components. Not surprisingly, conventional artificial neural networks (ANNs) have difficulty in modeling 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, higher-order neural networks (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 (P[T]HONNs), we introduce the concept of HONN groups. The latter incorporate piecewise continuous-activation functions and thresholds, and as a result are capable of modeling discontinuous (or piecewise-continuous) data, and what is more to any degree of accuracy. Several other PHONN variants are also described. The performance of P(T)HONN and HONN groups on representative financial time series is described (i.e., 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.
Convolutional neural networks for modeling and forecasting nonlinear nonstationary processes
