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A new seasonal cycle GM (1,1) model and its application in railway passenger volume forecasting

Huan Wang (School of Business, Jiangnan University, Wuxi, China)
Yuhong Wang (School of Business, Jiangnan University, Wuxi, China)
Dongdong Wu (School of Business, Jiangnan University, Wuxi, China)

Grey Systems: Theory and Application

ISSN: 2043-9377

Article publication date: 29 April 2021

Issue publication date: 28 February 2022




To predict the passenger volume reasonably and accurately, this paper fills the gap in the research of quarterly data forecast of railway passenger volume. The research results can also provide references for railway departments to plan railway operation lines reasonably and efficiently.


This paper intends to establish a seasonal cycle first order univariate grey model (GM(1,1) model) combing with a seasonal index. GM (1,1) is termed as the trend equation to fit the railway passenger volume in China from 2014 to 2018. The railway passenger volume in 2019 is used as the experimental data to verify the forecasting effect of the proposed model. The forecasting results of the seasonal cycle GM (1,1) model are compared with the traditional GM (1,1) model, seasonal grey model (SGM(1,1)), Seasonal Autoregressive Integrated Moving Average (SARIMA) model, moving average method and exponential smoothing method. Finally, the authors forecast the railway passenger volume from 2020 to 2022.


The quarterly data of national railway passenger volume have a clear tendency of cyclical fluctuations and show an annual growth trend. According to the comparison of the modeling results, the authors know that the seasonal cycle GM (1,1) model has the best prediction effect with the mean absolute percentage error of 1.32%. It is much better than the other models, reflecting the feasibility of the proposed model.


As the previous grey prediction model could not solve the series prediction problem with seasonal fluctuation, and there are few research studies on quarterly railway passenger volume forecasting, GM (1,1) model is taken as the trend equation and combined with the seasonal index to construct a combination forecasting model for accurate forecasting results in this study. Besides, considering the impact of the epidemic on passenger volume, the authors introduce a disturbance factor to deal with the forecasting results in 2020, making the modeling results more scientific, practical and referential.



The research reported in this paper was partially supported by the National Natural Science Foundation of China (71871106) and the Fundamental Research Funds for the Central Universities (JUSRP1809ZD; 2019JDZD06). The work was also sponsored by the major projects of Educational Science Fund of Jiangsu Province in 13th Five-Year Plan (A/2016/01); the key project of philosophy and social science research in Universities of Jiangsu Province (2018SJZDI051) and the Grey System Theme Innovation Zone Project (GS2019005).


Wang, H., Wang, Y. and Wu, D. (2022), "A new seasonal cycle GM (1,1) model and its application in railway passenger volume forecasting", Grey Systems: Theory and Application, Vol. 12 No. 2, pp. 293-317.



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