Model comparison of GM(1,1) and DGM(1,1) based on Monte-Carlo simulation

Discrete grey model (DGM(1,1)) is considered to be superior to grey model (GM(1,1)) because it can completely simulate the pure exponential sequences. However, owing to practical data generation process is interfered by random factors, the superiority of DGM(1,1) model to GM(1,1) model cannot be widely and reliably validated in practical applications. Therefore, by utilizing the Monte-Carlo simulation method, groups of completely random sequences conforming to different distributions are randomly generated and the predictive capabilities of the two models are compared. In addition, the novel grey models of fractional order accumulation (FGM(1,1) and FDGM(1,1)) are introduced for further comparison. The results show that the predictive capabilities of the two models for random sequences conforming to normal distribution are nearly equivalent. However, the predictive capabilities of DGM(1,1) model for the other three kinds of random sequences are all superior to those of GM(1,1) model. The parameters change of completely random sequences influences the predictive capabilities of the two models. The parameters change of random sequences with exponential trend can influence the predictive capability of GM(1,1) model while has no significant influence on the predictive capability of DGM(1,1) model. (C) 2019 Elsevier B.V. All rights reserved.