This study aims to address the issues of overfitting and underutilization of new information in traditional grey models for multi-frequency traffic flow forecasting. It proposes the Recursive Grey Multi-frequency Fourier Model (RGMFM) to enhance the extraction of multi-frequency periodic features and enable dynamic updating, thereby improving the accuracy and stability of short-term predictions for small-sample, multi-frequency traffic flow data.
The RGMFM integrates Fast Fourier Transform (FFT) and a recursive regression algorithm into the grey modeling framework. FFT extracts primary and secondary periodic components, while recursive regression prioritizes parameter updates with new data. The model incorporates two controllable parameters—an energy threshold and a memory factor—to simultaneously optimize its structure and parameter updating mechanism.
Simulation and experimental results demonstrate that RGMFM significantly outperforms benchmarks (SARIMA, LSTM, Transformer), reducing average RMSE by approximately 17% on 50 subsets of the PEMS08 dataset. It accurately captures daily and peak-hour traffic patterns and maintains robust performance under varying noise levels, validating its effectiveness and stability for multi-frequency forecasting.
The main originality lies in the novel hybrid framework that embeds signal processing (FFT) and recursive learning into grey system theory. The introduction of dual controllable parameters for integrated optimization provides a new, tunable, and interpretable modeling paradigm. This work extends grey models' applicability to complex, dynamic multi-frequency forecasting tasks, offering significant practical value for intelligent transportation systems and similar domains.
