A novel multi-variable grey forecasting model and its application in forecasting the grain production in China

In the multi-variable grey forecasting model GM(1,N), the extreme value of the independent variable is one of the important factors that affect the simulation and prediction results of the dependent variable. In this study, a smooth generation method was used to weaken the influence of the extreme value on the performance of GM(1,N), and a novel multi-variable grey forecasting model NMGM(1,N) based on the smooth generation of independent variable sequences with variable weights was constructed. The parameters of NMGM(1,N) were estimated and proved, and the time-response expression and the final restored expression of NMGM(1,N) were deduced. Besides, the detailed modeling steps were provided, and a MATLAB program for building the new model was developed. Moreover, the evaluation criteria of the model were introduced, and numerical examples were used to test the performance of the model. Lastly, the new model was applied to forecast China’s grain production. The global mean relative percentage error of the new model was only 0.689%, in comparison with the ones obtained from the GM(1,N), GM(0,N) and OGM(1,N), which were 4.268%, 3.480% and 1.302% respectively. The findings show that the new model has the best performance, which confirms the effectiveness of the structure improvement.