A novel multi-variable grey forecasting model and its application in forecasting the amount of motor vehicles in Beijing

- A novel multi-variable grey forecasting model, NGM(1,N), is proposed.
- A linear correction item and a grey action quantity item are introduced in GM(1,N).
- The NGM(1,N) has a better structure and performance than those of other grey models.
- The amount of motor vehicles in Beijing is effectively forecasted using NGM(1,N).

The structure defect of the GM(1,N) model is the major reason for its low simulation and prediction performance. To address this issue, a linear correction item h1(k − 1) and a grey action quantity h2 are introduced into the GM(1,N) model to improve its structure in this paper. Specifically, the 'h1(k − 1)' reflects the linear relations between the dependent variable and the independent variables, and the 'h2' shows the data change law of the dependent variable sequence. Based on this, a novel multi-variable grey forecasting model, NGM(1,1), is proposed. Furthermore, the NGM(1,N) model's time-response expression and the final restored expression are proved, its initial value is optimized, and a MATLAB program for building the NGM(1,N) model is developed. Lastly the NGM(1,N) model is applied to simulate and forecast the amount of Beijing's motor vehicles. The mean relative simulation and prediction percentage errors of the new model are only 0.009% and 1.149%, in comparison with the ones obtained from the traditional GM(1,N) model and the classical DGM(1,1) model, which are 4.680%, 10.685% and 4.411%, 11.167% respectively. The findings show that the new model has the best performance, which confirms the effectiveness of the structure improvement.