A non-linear grey Fourier model based on kernel method for seasonal traffic speed forecasting

This article introduces a non-linear grey Fourier model utilizing the kernel method to better characterize seasonal traffic speed with fluctuating trends. The linear trend term in the grey Fourier model is replaced with feature mapping, resulting in a non-linear form. Utilizing Lagrange multipliers and a kernel function, the parameter estimation is transformed into a linear equation-solving problem. Order selection is carried out via power spectrum analysis, and hyper-parameters are determined using Bayesian optimization. Two numerical examples from real problems are presented to validate the model's performance. The results indicate that the developed model outperforms nine models across four categories. Specifically, the model is applied to predict traffic speed in Guangzhou, and comparative results with four neural networks demonstrate its commendable performance.