An optimized discrete grey multi-variable convolution model and its applications

The grey multi-variable convolution model (GMC(1, N)) is a quality improvement of the traditional grey multi-variable prediction model (GM(1, N)) and has been successfully applied in many practical problems. However, the GMC(1, N) model still has some defects in several aspects; for instance, parameter estimation, simple model structure, and so on. To further improve the prediction accuracy and enhance the stability of the GMC(1, N) model, an optimized discrete GMC(1, N) model (ODGMC(1, N)) is proposed in this paper. In particular, a linear correction item is introduced in the new model, the parameters are computed consistently with the modeling process and the time response function of the new model is simply derived by the recursive method. The new proposed ODGMC(1,N) model not only can adjust the relationships between dependent variables and independent variables, but also show better stability than the GMC(1, N) model and its discrete form. Three numerical examples from different application fields are presented to confirm our findings. Numerical results show that the proposed ODGMC(1, N) model has both better fitting accuracy and prediction accuracy than the traditional GM(1, N) model, the GMC(1, N) model and their discrete forms, whether the sequence of dependent variable is increasing, deceasing, or fluctuating.