Applications of HONNs in Economics, Finance, and Accounting
Many researchers in the economics, finance, and accounting areas use artificial neural networks in their studies, however, only a few studies use HONN. Lee, Lee, and Park (1992) use HONNs to identify and control the nonlinear dynamic systems. The computer simulation results reveal that HONN models are more effective in controlling nonlinear dynamic systems. Karayiannis and Venetsanopoulos (1995) study the architecture, training, and properties of neural networks of order higher than one. They also study the formulation of the training of HONNs as a nonlinear associative recall problem that provides the basis for their optimal least squares training. Bouzerdoum (1999) presents a class of HONNs, shunting inhibitory artificial neural networks (SIANNs). These HONNs can produce classifiers with complex nonlinear decision boundaries, ranging from simple hyperplanes to very complex nonlinear surfaces. The author also provides a training method for SIANNs. Li, Hirasawa, and Hu (2003) present a constructive method for HONNs with multiplication units. The proposed method provides a flexible mechanism for incremental network growth.
Zhang, Zhang, and Fulcher (1997) develop trigonometric polynomial higher order neural network (THONN) group models for financial data prediction. Results show that THONN group models can handle nonlinear data that has discontinuous points. Xu and Zhang (1999) develop adaptive HONNs with adaptive neuron functions to approximate continuous data. Lu, Zhang, and Scofield (2000) generate Polynomial and Trigonometric Higher Order Neural Network (PTHONN) models for multi-polynomial function simulation. Crane and Zhang (2005) provide a SINC Higher Order Neural Network (SINCHONN) models, which use SINC function as active neurons. These models successfully simulate currency exchange rates.
Ghazali (2005) use HONN for financial time series prediction and find HONN outperforms traditional multilayer neural network models. Knowles, Hussain, Deredy, Lisboa, and Dunis (2005) use HONNs with Bayesian confidence measure for prediction of EUR/USD exchange rates. They show that the simulation results for HONNs are 8% better than multilayer neural network. In the accounting area, Zhang (2005) uses HONN to estimate misclassification cost for different financial distress prediction models. Moreover, HONN has been used to generate nonlinear models for the power of chief elected officials and debt (Zhang, 2006). Dunis, Laws, and Evans (2006) use HONN to build a nonlinear model for modeling and trading the gasoline crack spread. The results show that the spread does indeed exhibit asymmetric adjustment, with movements away from fair value being nearly three times larger on the downside than on the upside.
Zhang, Murugesan and Sadeghi (1995), and Zhang, Zhang and Keen (1999) use both Polynomial and Trigonometric HONNs to simulate and predict financial time series data from the Reserve Bank of Australia Bulletin www.abs.gov.au/ausstats/abs@.nsf/w2.3 to around 90% accuracy. Zhang and Lu (2001) develop the Polynomial and Trigonometric HONN (PTHONN) and Multiple Polynomial functions HONN (MPHONN) models for improved performance. In financial time series prediction, PHONN groups produce around 1.2% error for simulation compared with 11% for HONNs (Zhang, Zhang, and Fulcher, 2000). Improvements in performance are also observed with THONN groups (Zhang, Zhang, and Fulcher, 2000). Currently, multi-PHONN (Zhang 2001, 2002, 2005, and 2006) is capable of simulating not only polynomial and/or trigonometric functions, but also a combination of these and sigmoid and/or logarithmic functions. As a result, they can better approximate real-world economic time series data.