Artificial Polynomial and Trigonometric Higher Order Neural Network Group Models

Abstract

Real world financial data is often discontinuous and non-smooth. Accuracy will be a problem, if we attempt to use neural networks to simulate such functions. Neural network group models can perform this function with more accuracy. Both Polynomial Higher Order Neural Network Group (PHONNG) and Trigonometric polynomial Higher Order Neural Network Group (THONNG) models are studied in this chapter. These PHONNG and THONNG models are open box, convergent models capable of approximating any kind of piecewise continuous function to any degree of accuracy. Moreover, they are capable of handling higher frequency, higher order nonlinear, and discontinuous data. Results obtained using Polynomial Higher Order Neural Network Group and Trigonometric polynomial Higher Order Neural Network Group financial simulators are presented, which confirm that PHONNG and THONNG group models converge without difficulty, and are considerably more accurate (0.7542% - 1.0715%) than neural network models such as using Polynomial Higher Order Neural Network (PHONN) and Trigonometric polynomial Higher Order Neural Network (THONN) models.