A novel multivariate grey system model with conformable fractional derivative and its applications

• A novel conformable fractional derivative multivariate grey model is developed. • The ant lion optimization algorithm is used to search optimal conformable fractional derivative. • The urban consumption per capita of China are studied by different forecasting models. • Some statistical analysis methods are performed to show the effectiveness and stability of the proposed model. To further improve the effectiveness and precision of multivariate time series forecasting, a conformable fractional derivative multivariate grey system model is proposed in this work. Firstly, the general solution of the model is deduced by the grey theory, the definition of the conformable fractional derivative, the theory of ordinary differential equations and the two-point trapezoidal approximation formula. Then the ordinary least squares estimation method is utilized to derive linear system parameters, and the ant lion optimizer algorithm is used to search the optimal fractional order. Finally the newly constructed model is applied to forecast the urban consumption per capita of China. The total mean absolute percentage error of the new model is only 0.6434%, in comparison with ones obtained from GM(1,1), DGM(1,1), CFGM(1,1), CFNGM ( 1 , 1 , k , c ) , CFGM ( 1 , 1 , D ) , MLR, GMC T ( 1 , N ) , RDGM ( 1 , N ) , FGMC ( 1 , N ) and GMC ( r , N ) , which are 4.0334%, 4.0837%, 3.4751%, 3.6629%, 2.2129%, 1.0487%, 784.1107%, 1.0168%, 0.7655% and 0.7954% respectively. The results show the new model has a better performance compared with other models.