Forecasting Oil Consumption with Novel Fractional Grey Prediction Model Based on Simpson Formula

Main Article Content

Xiwang Xiang
Peng Zhang
Lang Yu


With the development of human society, the evolving transition of energy will become a common challenge that mankind has to face together. In this context, it is crucial to make scientific and reasonable predictions about energy consumption. This paper presents a novel fractional grey prediction model FGM(1,1,k2) based on the classical fractional grey system theory. In order to improve the prediction accuracy of the FGM(1,1,k2) model, we further analyze the model error and propose improved grey model called as SFGM with optimization of background value. The numerical cases point out that SFGM(1,1,k2) significantly outperforms other existing fractional grey models. Finally, the proposed SFGM(1,1,k2) is applied to the forecasting of oil consumption, the predicted results would provide a reference for making energy policy in new situations.

Energy economic, fractional grey system, SFGM model, Simpson formula.

Article Details

How to Cite
Xiang, X., Zhang, P., & Yu, L. (2019). Forecasting Oil Consumption with Novel Fractional Grey Prediction Model Based on Simpson Formula. Asian Research Journal of Mathematics, 15(2), 1-27.
Original Research Article


Deng JL. Control problems of grey systems [J]. Sys. & Contr. Lett. 1982;1(5):288-294.

Ene S, Öztürk N. Grey modelling based forecasting system for return flow of end-of-life vehicles [J]. Technological Forecasting and Social Change. 2017;115:155-166.

Wang Q, Liu L, Wang S, et al. Predicting Beijing's tertiary industry with an improved grey model [J]. Applied Soft Computing. 2017;57:482-494.

Ding S. A novel discrete grey multivariable model and its application in forecasting the output value of China’s high-tech industries [J]. Computers & Industrial Engineering. 2019;127:749-760.

Ma X, Liu Z, Wang Y. Application of a novel nonlinear multivariate grey Bernoulli model to predict the tourist income of China [J]. Journal of Computational and Applied Mathematics. 2019;347:84-94.

Kayacan E, Ulutas B, Kaynak O. Grey system theory-based models in time series prediction [J]. Expert Systems with Applications. 2010;37(2):1784-1789.

Ma X, Mei X, Wu W, et al. A novel fractional time delayed grey model with Grey Wolf Optimizer and its applications in forecasting the natural gas and coal consumption in Chongqing China [J]. Energy. 2019;178:487-507.

Ma X, Liu Z. The kernel-based nonlinear multivariate grey model [J]. Applied Mathematical Modelling. 2018;56:217-238.

Wu W, Ma X, Zeng B, et al. Forecasting short-term renewable energy consumption of China using a novel fractional nonlinear grey Bernoulli model [J]. Renewable Energy. 2019;140:70-87.

Ding S, Hipel K W, Dang Y. Forecasting China's electricity consumption using a new grey prediction model [J]. Energy. 2018;149:314-328.

Zhang W, Xiao R, Shi B, et al. Forecasting slope deformation field using correlated grey model updated with time correction factor and background value optimization [J]. Engineering Geology. 2019;105215.

Yang Y, Xue D. An actual load forecasting methodology by interval grey modeling based on the fractional calculus [J]. ISA Transactions. 2018;82:200-209.

Zhao H, Guo S. An optimized grey model for annual power load forecasting [J]. Energy. 2016;107: 272-286.

Ou S L. Forecasting agricultural output with an improved grey forecasting model based on the genetic algorithm [J]. Computers and Electronics in Agriculture. 2012;85:33-39.

Guan-Jun TAN. The Structure Method and Application of Background Value in Grey System GM (1, 1) Model (Ⅰ) [J]. Systems Engineering-Theory & Practice. 2000;4.

Guan-Jun T. The Structure Method and Application of Background Value in Grey System GM (1, 1) Model (Ⅱ) [J]. Systems Engineering-Theory & Practice. 2000;5.

Wang Y N. An extended step by step optimum direct modeling method of GM (1, 1)[J]. Systems Engineering Theory & Practice. 2003;23(2):120-124.

Dang L, Sifeng L, el. The optimization of grey model GM (1,1) [J]. Engineering Science. 2003;08:50-53.

Tang W, Xiang C. The improvements of forecasting method in GM (1, 1) model based on quadratic interpolation [J]. Chinese Journal of Management Science. 2006;6:109-112.

Li J F, Dai W Z. A new approach of background value-building and its application based on data interpolation and Newton-Cores formula [J]. Systems Engineering Theory & Practice. 2004;24(10): 122-126.

He M X, Wang Q. Constructing the background value for GM (1, 1) model based on Simpson formula [J]. Journal of Quantitative Economics. 2011;4:101-104.

Wu F, Shi K, Yiziteliopu N, et al. Based on simpson formula improved non-interval GM (1, 1) model and application[C]. Proceedings of the 32nd Chinese Control Conference. IEEE. 2013;8431-8435.

Cuifeng L I, Wenzhan D A N. Determinator of the background level in the non-equidistant GM (11) model [J]. Journal of Tsinghua University (Science and Technology), Beijing. 2007;47(s2):1729-1732.

Wang Y M, Dang Y G, Wang Z X. The optimization of background value in non-equidistant GM (1, 1) model [J]. Chinese Journal of Management Science. 2008;16(4):159-162.

He M X, Wang Q. New algorithm for GM (1, N) modeling based on Simpson formula [J]. Systems Engineering-Theory & Practice. 2013;33(1):199-202.

Shen Y, Sun H. Optimization of background values of GM (1, N) model and its application [J]. Journal of Information Processing and Management. 2013;4(1):58-64.

Wu L, Liu S, Yao L, et al. Grey system model with the fractional order accumulation [J]. Communications in Nonlinear Science and Numerical Simulation. 2013;18(7):1775-1785.

Wu L F, Li N, Zhao T. Using the seasonal FGM (1, 1) model to predict the air quality indicators in Xingtai and Handan [J]. Environmental Science and Pollution Research. 2019;26(14):14683-14688.

Wu L, Zhao H. Using FGM (1, 1) model to predict the number of the lightly polluted day in Jing-Jin-Ji region of China [J]. Atmospheric Pollution Research. 2019;10(2):552-555.

Wu L, Gao X, Xiao Y, et al. Using a novel multi-variable grey model to forecast the electricity consumption of Shandong Province in China [J]. Energy. 2018;157:327-335.

Xiao X, Guo H, Mao S. The modeling mechanism, extension and optimization of grey GM (1, 1) model [J]. Applied Mathematical Modelling. 2014;38(5-6):1896-1910.

Mao S, Gao M, Xiao X, et al. A novel fractional grey system model and its application [J]. Applied Mathematical Modelling. 2016;40(7-8):5063-5076.

Wu W, Ma X, Zeng B, et al. Application of the novel fractional grey model FAGMO (1, 1, k) to predict China's nuclear energy consumption [J]. Energy. 2018;165:223-234.

Jie Cui, Si-feng Liu, Bo Zeng, Nai-ming Xie. A novel grey forecasting model and its optimization. Applied Mathematical Modelling. 2013;37(6):4399-4406.

Zeng B, Meng W, Tong M. A self-adaptive intelligence grey predictive model with alterable structure and its application [J]. Engineering Applications of Artificial Intelligence. 2016;50:236-244.