Fractional High Frequency Cosine and Sine Higher Order Neural Network for Economics

The data in the real world are complex and varied. When we apply artificial neural networks to simulate the real-world commerce data through simple functions, accuracy could become problematic. To overcome this issue, we could choose Higher Order Neural Network (HONN) models, which can simulate a data set very accurately. This paper has developed a new open-box HONN model with fractional functions, called a Fractional High Frequency Cosine and Sine HONN (FHFCSHONN) model. FHFCSHONN structure and learning algorithm formulas are studied too. This paper also built a new software package called a FHFCSHONN simulator. Based on the commerce data testing results, the FHFCSHONN model's average error is 0.6980%, while the other three HONN model average errors are 4.0160%, 4.2370%, and 4.3556% respectively.