Research on a novel fractional GM(α, n) model and its applications

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.

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.

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.

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.

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.