Higher Order Neural Networks with Bayesian Confidence Measure for the Prediction of the EUR/USD Exchange Rate

Abstract

Multi-Layer Perceptrons (MLP) are the most common type of neural network in use, and their ability to perform complex nonlinear mappings and tolerance to noise in data is well documented. However, MLPs also suffer long training times and often reach only local optima. Another type of network is Higher Order Neural Networks (HONN). These can be considered a ‘stripped-down’ version of MLPs, where joint activation terms are used, relieving the network of the task of learning the relationships between the inputs. The predictive performance of the network is tested with the EUR/USD exchange rate and evaluated using standard financial criteria including the annualized return on investment, showing a 8% increase in the return compared with the MLP. The output of the networks that give the highest annualized return in each category was subjected to a Bayesian based confidence measure. This performance improvement may be explained by the explicit and parsimonious representation of high order terms in Higher Order Neural Networks, which combines robustness against noise typical of distributed models, together with the ability to accurately model higher order interactions for long-term forecasting. The effectiveness of the confidence measure is explained by examining the distribution of each network’s output. We speculate that the distribution can be taken into account during training, thus enabling us to produce neural networks with the properties to take advantage of the confidence measure.