Improved multi-variable grey forecasting model with a dynamic background-value coefficient and its application

In grey system theory, the value of the background-value coefficient has a significant impact on the performance of a multi-variable grey forecasting model (MGFM). However, for most existing MGFMs, the background-value coefficient is fixed at 0.5 to simplify the modelling process. For this, a new MGFM model is proposed, which is based on a dynamic background-value coefficient. Then, the time response function and the final restored expression of the new MGFM model are deduced, proved and simplified by a Gaussian function. After this, the dynamic background-value coefficient is optimized by the Particle Swarm Optimization algorithm. To evaluate the performance of the new model, the Mean Relative Simulation Percentage Errors (MRSPEs) of the new MGFM model are compared with those of models with other background-value coefficients for three typical cases. The results show that the new MGFM model outperforms the raw MGFM models with other background-value coefficients. In addition, the closer the background value coefficient is to the optimal coefficient, the smaller the MRSPE is and the better the model performs. Lastly, the new model is employed to simulate and forecast the number of users of wireless communications in China. The findings demonstrate that the new MFGM model achieves the best performance, which confirms the effectiveness of background-value optimization in a multi-variable grey forecasting model.