The novel fractional discrete multivariate grey system model and its applications

• Published in: Applied Mathematical Modelling Vol. 70; pp. 402 - 424
• Main Authors: Ma, Xin, Xie, Mei, Wu, Wenqing, Zeng, Bo, Wang, Yong, Wu, Xinxing
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.06.2019; Elsevier BV
• Subjects: Accumulation; Algorithms; China’s economics; Convolution; Convolution integrals; Discrete grey model; Fractional order accumulation; Grey system model; Grey Wolf Optimizer; Mathematical analysis; Model accuracy; Discrete grey model; Grey system model; China’s economics; Grey Wolf Optimizer; Fractional order accumulation
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2019.01.039

•A novel fractional discrete multivariate grey model is proposed.•The proposed model is proved to be an unbiased model theoretically.•A revised Grey Wolf Optimizer is introduced to optimize the fractional order.•The proposed model outperforms other nine grey models in four case studies.•The proposed model presents high potential in real world applications. Fractional order accumulation is a novel and popular tool which is efficient to improve accuracy of the grey models. However, most existing grey models with fractional order accumulation are all developed on the conventional methodology of grey models, which may be inaccurate in the applications. In this paper an existing fractional multivariate grey model with convolution integral is proved to be a biased model, and then a novel fractional discrete multivariate grey model based on discrete modelling technique is proposed, which is proved to be an unbiased model with mathematical analysis and stochastic testing. An algorithm based on the Grey Wolf Optimizer is introduced to optimize the fractional order of the proposed model. Four real world case studies with updated data sets are executed to assess the effectiveness of the proposed model in comparison with nine existing multivariate grey models. The results show that the Grey Wolf Optimizer-based algorithm is very efficient to optimize the fractional order of the proposed model, and the proposed model outperforms other nine models in the all the real world case studies.