This chapter discusses the use of two artificial Higher Order Neural Networks (HONNs) models; the Pi- Sigma Neural Networks and the Ridge Polynomial Neural Networks, in financial time series forecasting. The networks were used to forecast the upcoming trends of three noisy financial signals; the exchange rate between the US Dollar and the Euro, the exchange rate between the Japanese Yen and the Euro, and the United States 10-year government bond. In particular, we systematically investigate a method of pre-processing the signals in order to reduce the trends in them. The performance of the networks is benchmarked against the performance of Multilayer Perceptrons. From the simulation results, the predictions clearly demonstrated that HONNs models, particularly Ridge Polynomial Neural Networks generate higher profit returns with fast convergence, therefore show considerable promise as a decision making tool. It is hoped that individual investor could benefit from the use of this forecasting tool.
Application Of Pi-Sigma Neural Networks And Ridge Polynomial Neural Networks To Financial Time Series Prediction
There are numerous research works being carried out in the area of neural networks, however not all of these research works can be used in real commercial applications. This is probably due to the size of the neural networks which can be large enough to prevent the problem solution from being used in real world problems. Furthermore, the large network size can slow down the training speed and its convergence.
The highly popularized Multilayer Perceptrons (MLPs) models have been successfully applied in financial time series forecasting. A review on existing literature reveals financial studies on a wide variety of subjects such as stock price forecasting (Castiglione, 2000; Chan, Wong, & Lam, 2000; Zekić, 1998), currency exchange rate forecasting (Chen & Leung, 2005; Gradojevic & Yang, 2000; Yao & Tan, 2000; Yao, Poh, & Jasic, 1996; Kuan & Liu, 1995), returns prediction (Dunis & Williams, 2002; Shachmurove & Witkowska, 2000; Franses, 1998), forecasting currency volatility (Yumlu, Gurgen, & Okay, 2005; Dunis & Huang, 2002), sign prediction (Fernandez-Rodriguez, Gonzalec-Martel, & Sosvilla-Rivero, 2000). Since MLPs structure is multilayered and the Backpropagation algorithm involves high computational complexity, this structure requires excessive training time for learning. Further, the number of weights and in turn the training time increases as the number of layers and the nodes in a layer increases (Patra & Pal, 1995; Chen & Leung, 2004).
Concerned with the slow learning problems of MLPs, this chapter investigates the use of artificial Higher Order Neural Networks (HONNs) which have a fast learning properties and powerful mapping of single layer trainable weights networks in financial time series prediction. Higher Order Neural Networks distinguish themselves from ordinary feedforward networks by the presence of higher order terms in the network. In a great variety of Neural Networks models, neural inputs are combined using the summing operation. HONNs in contrast contain not only summing unit, but also units that multiply their inputs which referred to higher order terms or product units.
Although most neural network models share a common goal in performing functional mapping, different network architectures may vary significantly in their ability to handle different types of problems. For some tasks, higher order combinations of some of the inputs or activations may be appropriate to help form good representation for input-output mapping. Two types of HONNs; the Pi-Sigma Neural Networks and the Ridge Polynomial Neural Networks were used as nonlinear predictor to capture the underlying movement in financial time series signals and to predict the future trend in the financial market.