A novel simultaneous grey model parameter optimization method and its application to predicting private car ownership and transportation economy

Common models used for grey system predictions include the GM (1, 1), GM (1, N), and GM (N, 1). Their whitening equations are ordinary differential equations. However, the objects and factors are generally characterized by mutual restrictions and variable interactions. Thus, the relationship cannot be adequately described using a single differential equation. Therefore, this paper proposes a novel simultaneous grey model. A parameter optimization method is developed, and the time response equation of a simultaneous grey model with 2 interactive variables is derived. The model has high simulation and prediction precision because the parameter optimization's objective function minimizes the average relative errors of the simulation and prediction. The proposed model with two mutually influencing variables is used to predict the private car ownership and the added value of the transportation industry in China. The results indicate that the simultaneous grey model has significantly higher precision than the conventional single grey model. The novel model and method improve the grey modeling system and are significant for in-depth studies, popularization, and application of grey models.