A novel grey prediction model based on quantile regression

Abstract To solve the problem that existing grey prediction models are prone to be affected by outliers and show poor stability, a novel grey prediction model based on quantile regression technology is proposed (abbreviated as the QGM(1,1) model). The improved simplex algorithm is utilized to solve the programming problem in the model so that the structural parameters are estimated at different quantiles. Compared with the parameters estimation of traditional grey prediction models, the QGM(1,1) model describes the influence of the independent variable on the range of the dependent variable and the shape of the conditional distribution accurately, and captures the tail characteristics of the distribution. Moreover, the results of interval prediction are given according to the estimated values of parameters at different quantiles by setting a corresponding error criterion. The effectiveness of the novel model is verified by three analytical examples. The results show that the QGM(1,1) model not only can conclude the predicted value of the distribution center but also can predict the dynamic trends of upper and lower limits of the distribution. The prediction accuracy is significantly improved and the robustness is greatly enhanced.