Neuron-adaptive higher order neural-network models for automated financial data modeling

TLDR

Financial data are nonlinear, high‑frequency, and discontinuous, making them difficult to model with classical neural networks that cannot automatically select optimal model order. The study develops neuron‑adaptive higher‑order neural‑network (NAHONN) models to automatically select optimal model structure for financial data. The authors introduce 1‑D, 2‑D, and n‑D NAHONN architectures, a learning algorithm, and NAHONN Group (NAHONG) models to train these networks. NAHONNs and NAHONGs converge, universally approximate financial data, and automatically determine optimal model order, offering transparent, expert‑acceptable solutions.

Abstract

Real-world financial data is often nonlinear, comprises high-frequency multipolynomial components, and is discontinuous (piecewise continuous). Not surprisingly, it is hard to model such data. Classical neural networks are unable to automatically determine the optimum model and appropriate order for financial data approximation. We address this problem by developing neuron-adaptive higher order neural-network (NAHONN) models. After introducing one-dimensional (1-D), two-dimensional (2-D), and n-dimensional NAHONN models, we present an appropriate learning algorithm. Network convergence and the universal approximation capability of NAHONNs are also established. NAHONN Group models (NAHONGs) are also introduced. Both NAHONNs and NAHONGs are shown to be "open box" and as such are more acceptable to financial experts than classical (closed box) neural networks. These models are further shown to be capable of automatically finding not only the optimum model, but also the appropriate order for specific financial data.