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A novel grey prediction model based on quantile regression. (English) Zbl 1455.93105

Summary: 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.

MSC:

93C41 Control/observation systems with incomplete information
62P30 Applications of statistics in engineering and industry; control charts

Software:

CAViaR
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Full Text: DOI

References:

[1] Deng, J. L., The control problems of grey systems, Syst Control Lett, 5, 288-294 (1982) · Zbl 0482.93003
[2] Xie, N. M.; Liu, S. F., Discrete grey forecasting model and its optimization, Appl Math Modell, 33, 2, 1173-1186 (2009) · Zbl 1168.62380
[3] Wei, B. L.; Xie, N.; Yang, L., Understanding cumulative sum operator in grey prediction model with integral matching, Commun Nonlinear Sci NumerSimul, 82, 105076 (2020) · Zbl 1451.93211
[4] Ye, J.; Dang, Y. G.; Li, B. J., Grey-Markov prediction model based on background value optimization and central-point triangular whitenization weight function, Commun Nonlinear Sci NumerSimul, 54, 320-330 (2018) · Zbl 1510.62392
[5] Yuan, C. Q.; Liu, S. F.; Fang, Z. G., Comparison of China’s primary energy consumption forecasting by using ARIMA (the autoregressive integrated moving average) model and GM(1,1) model, Energy, 100, 384-390 (2016)
[6] Zeng, X. Y.; Shu, L.; Huang, G. M.; Jiang, J., Triangular fuzzy series forecasting based on grey model and neural network, Appl Math Modell, 40, 3, 1717-1727 (2016) · Zbl 1446.62257
[7] Akay, D.; Atak, M., Grey prediction with rolling mechanism for electricity demand of Turkey, Energy, 32, 9, 1670-1675 (2007)
[8] Zhao, Z.; Wang, J. Z.; Zhao, J.; Su, Z. Y., Using a grey model optimized by differential evolution algorithm to forecast the per capita annual net income of rural households in China, Omega, 40, 5, 525-532 (2012)
[9] Wu, L. F.; Liu, S. F.; Yao, L. G.; Yan, S. L., Grey system model with the fractional order accumulation, Commun Nonlinear Sci NumerSimul, 18, 1775-1785 (2013) · Zbl 1274.62639
[10] Mao, S. H.; Gao, M. Y.; Xiao, X. P.; Zhu, M., A novel fractional grey system model and its application, Appl Math Modell, 40, 5063-5076 (2016) · Zbl 1459.62180
[11] Ma, X.; Xie, M.; Wu, W. Q.; Zeng, B.; Wang, Y.; Wu, X. X., The novel fractional discrete multivariate grey system model and its applications, Appl Math Modell, 70, 402-424 (2019) · Zbl 1464.62389
[12] Zeng, B.; Duan, H. M.; Zhou, Y. F., A new multivariable grey prediction model with structure compatibility, Appl Math Modell, 75, 385-397 (2019) · Zbl 1481.62073
[13] Chen, C. I.; Chen, H. L.; Chen, S. P., Forecasting of foreign exchange rates of Taiwan’s major trading partners by novel nonlinear grey Bernoulli model NGBM, Commun Nonlinear Sci NumerSimul, 13, 6, 1194-1204 (2008)
[14] Wang, Z. X.; Hipel, K. W.; Wang, Q.; He, S. W., An optimized NGBM(1,1) model for forecasting the qualified discharge rate of industrial wastewater in China, Appl Math Modell, 35, 12, 5524-5532 (2011)
[15] Zhou, J.; Fang, R.; Li, Y., Parameter optimization of nonlinear grey Bernoulli model using particle swarm optimization, Appl Math Comput, 207, 2, 292-299 (2009) · Zbl 1158.65307
[16] Hsin, P. H.; Chen, C. I., Application of game theory on parameter optimization of the novel two-stage Nash nonlinear grey Bernoulli model, Commun Nonlinear Sci NumerSimul, 27, 1-3, 168-174 (2015) · Zbl 1457.91123
[17] Hsin, P. H.; Chen, C. I., Application of trembling-hand perfect equilibrium to Nash nonlinear grey Bernoulli model: an example of BRIC’s GDP forecasting, Neural Comput Appl, 28, 1, 269-274 (2017)
[18] Ma, X.; Hu, Y. S.; Liu, Z. B., A novel kernel regularized nonhomogeneous grey model and its applications, Commun Nonlinear Sci NumerSimul, 48, 51-62 (2017) · Zbl 1510.62391
[19] Xiong, P. P.; Yan, W. J.; Wang, G. Z.; Pei, L. L., Grey extended prediction model based on IRLS and its application on smog pollution, Appl Soft Comput, 80, 797-809 (2019)
[20] Buchinsky, M., Changes in the U.S. wage structure 1963-1987: application of quantile regression, Econometrica, 62, 2, 405 (1994) · Zbl 0800.90235
[21] Koenker, R.; Bassett, J. G., Regression quantiles, Econometrica, 46, 33-50 (1978) · Zbl 0373.62038
[22] Washington, S.; Haque, M.; Oh, J.; Lee, D., Applying quantile regression for modeling equivalent property damage only crashes to identify accident blackspots, Accid Anal Prev, 66, 136-146 (2014)
[23] Cade, B. S.; Noon, B. R., A gentle introduction to quantile regression for ecologists, Front Ecol Environ, 1, 8, 412-420 (2003)
[24] Engle, R. F.; Manganelli, S., CAViaR: Conditional autoregressive value at risk by regression quantiles, J Bus Econ Stat, 22, 4, 367-381 (2004)
[25] Li, Q.; Xi, R.; Lin, N., Bayesian regularized quantile regression, Bayesian Anal, 5, 3, 553-556 (2010) · Zbl 1330.62143
[26] Wang, Z. X.; Zhang, H. L.; Zheng, H. H., Estimation of lorenz curves based on dummy variable regression, Econ Lett, 69-75 (2019) · Zbl 1416.62684
[27] Koenker, R.; Machado, J. A.F., GMM inference when the number of moment conditions is large, J Econom, 93, 2, 327-344 (1999) · Zbl 0941.62077
[28] Lewis, C. D., Industrial and business forecasting methods (1982), Butterworth Scientific: Butterworth Scientific London
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