Expansion modelling of discrete grey model based on multi-factor information aggregation

This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h variables grey forecasting model (GM (1, h)), always aggregate the main system variable and independent variables in a linear form rather than a nonlinear form, while a nonlinear form could be used in more cases than the linear form. And the nonlinear form could aggregate collinear independent factors, which widely lie in many multi-factor forecasting problems. To overcome this problem, a new approach, named as the Solow residual method, is proposed to aggregate independent factors. And a new expansion model, feedback multi-factor discrete grey forecasting model based on the Solow residual method (abbreviated as FDGM (1, h)), is proposed accordingly. Then the feedback control equation and the parameters' solution of the FDGM (1, h) model are given. Finally, a real application is used to test the modelling accuracy of the FDGM (1, h) model. Results show that the FDGM (1, h) model is much better than the non-homogeneous discrete grey forecasting model (NDGM) and the GM (1, h) model.