Abstract
The Verhulst model is used in many natural and social systems. When simulating and predicting system sequences with an inverted U shape or a signal peak feature by the grey Verhulst model (abbreviated as GVM), such as the pig price index, a drift phenomenon happens sometimes. We introduce a grey generalized Verhulst model named as GGVM to address this problem. Compared with the GVM, the GGVM contains a constant as the grey action quantity. Besides, the multivariable grey generalized Verhulst model is also given. Three cases containing Glipizide tablets blood drug concentration series, the number of traffic deaths, and consumer price index (abbreviated as CPI) sequences are utilized to demonstrate that GGVM can eliminate the drift phenomenon effectively. Given that the pork is the most consumed meat for Chinese residents and the fluctuation of its price is closely related to the interests of residents and pig-breeding enterprises, it is important to predict the pork price. So the prediction of pork price index whose time series possesses an inverted U shape is carried out by GGVM, GVM, and intelligent algorithm models, including LSSVR, \(\varepsilon \)-SVR, and RBF in the empirical part. The results show that GGVM produces higher accurate simulation and prediction than the models as given above.
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References
Bishop C (1991) Improving the generalization properties of radial basis function neural networks. Neural Comput 3:579–588
Deng JL (1982) Control problems of grey system. Syst Control Lett 1(5):288–294
Ene S, Öztürk N (2017) Grey modelling based forecasting system for return flow of end-of-life vehicles. Technol Forecast Soc Change 115:155–166
Evans M (2014) An alternative approach to estimating the parameters of a generalised Grey Verhulst model: an application to steel intensity of use in the UK. Expert Syst Appl 41(4):1236–1244
Gu GL, Dai XY, Liu J (2015) Pork price prediction based on improved GM(1,1) model. J Zheng Zhou Uinv Light Ind 30(2):105–108
Han G, Yang BH, Yang SS (2005) Grey pharmacokinetics model of glipizide tablets in serum concentration. Math Pract Theory 35(5):85–87 (in Chinese)
He ZQ, Chai RH, Sang WG et al (1996) Dynamic prediction of forest fuel loads by grey Verhulst model. J Northeast For Univ 7(2):36–40
Kayacan E, Ulutas B, Kaynak O (2010) Grey system theory-based models in time series prediction. Expert Syst Appl 37(2):1784–1789
Kayacan E, Ulutas B, Kaynak O (2010) Grey system theory-based models in time series prediction. Expert Syst Appl 37(2):1784–1789
Li DC, Yeh CW, Chang CJ (2009) An improved grey-based approach for early manufacturing data forecasting. Comput Ind Eng 57(4):1161–1167
Liu SF, Lin Y (2006) Grey information theory and practical applications. Springer, London
Liu YR, Duan QL, Wang DJ et al (2019) Prediction for hog prices based on similar sub-series search and support vector regression. Comput Electron Agric 157:581–588
Ma XW, Zhu ZQ (2008) The grey neural network model and its application in pork price prediction. J Inner Mong Agric Univ 4(10):91–93
Ma W, Zhu X, Wang M (2013) Forecasting iron ore import and consumption of China using grey model optimized by particle swarm optimization algorithm. Resour Policy 38(4):613–620
Suykens JAK, Vandewalle J (1999) Least squares support vector machine classifiers. Neural Process Lett 9:293–300
Vapnik VN (1995) The nature of statistical learning theory. Springer Press, New York
Wang ZX, Ye DJ (2017) Forecasting Chinese carbon emissions from fossil energy consumption using non-linear grey multivariable models. J Clean Prod 142(2):600–612
Wang ZX, Ye DJ (2017) Forecasting Chinese carbon emissions from fossil energy consumption using non-linear grey multivariable models. J Clean Prod 142:600–612
Wu LF, Liu SF, Yang YJ (2016) Grey double exponential smoothing model and its application on pig price forecasting in China. Appl Soft Comput 39:117–123
Xie NM, Liu SF (2009) Discrete grey forecasting model and its optimization. Appl Math Model 33(2):1173–1186
Xie NM, Yuan CQ, Yang YJ (2015) Forecasting China’s energy demand and self-sufficiency rate by grey forecasting model and Markov model. Electric Power Energy Syst 66:1–8
Yao TX, Liu SF, Xie NM (2009) On the properties of small sample of GM (1,1) model. Appl Math Model 33(4):1894–1903
Zeng B, Luo C, Liu SF et al (2016) Development of an optimization method for the GM(1, N) model. Eng Appl Artif Intell 55:353–362
Zeng B, Luo CM, Liu SF, Li C (2016) A novel multi-variable grey forecasting model and its application in forecasting the amount of motor vehicles in Beijing. Comput Ind Eng 101:479–489
Zhao C (2010) The modeling and improvement of BP neural network prediction for the price of pork which combined with gray theory. Ji Lin Uinversity, Changchun
Zhao H, Guo S (2016) An optimized grey model for annual power load forecasting. Energy 107:272–286
Zhao Z, Wang J, Zhao J et al (2012) 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
Zhao HH, Jian LR, Liu Y et al (2014) Grey Verhulst model and application based on background value and initial value optimizations. Syst Eng 3:149–153 (in Chinese)
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This work was funded by the Research Initiation Fund of Changzhou University (Grant No. ZMF14020082).
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Zhou, W., Pei, L. The grey generalized Verhulst model and its application for forecasting Chinese pig price index. Soft Comput 24, 4977–4990 (2020). https://doi.org/10.1007/s00500-019-04248-0
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DOI: https://doi.org/10.1007/s00500-019-04248-0