Research on a novel fractional GM(<i>α</i>, <i>n</i>) model and its applications

Abstract

Purpose The purpose of this paper is to develop a novel multivariate fractional grey model termed GM( a , n ) based on the classical GM(1, n ) model. The new model can provide accurate prediction with more freedom, and enrich the content of grey theory. Design/methodology/approach The GM( α , n ) model is systematically studied by using the grey modelling technique and the forward difference method. The optimal fractional order a is computed by the genetic algorithm. Meanwhile, a stochastic testing scheme is presented to verify the accuracy of the new GM( a , n ) model. Findings The recursive expressions of the time response function and the restored values of the presented model are deduced. The GM(1, n ), GM( a , 1) and GM(1, 1) models are special cases of the model. Computational results illustrate that the GM( a , n ) model provides accurate prediction. Research limitations/implications The GM( a , n ) model is used to predict China’s total energy consumption with the raw data from 2006 to 2016. The superiority of the GM( a , n ) model is more freedom and better modelling by fractional derivative, which implies its high potential to be used in energy field. Originality/value It is the first time to investigate the multivariate fractional grey GM( α , n ) model, apply it to study the effects of China’s economic growth and urbanization on energy consumption.