SARIMA modelling approach for railway passenger flow forecasting
Abstract
In this paper, railway passenger flows are analyzed and a suitable modeling method proposed. Based on historical data composed from monthly passenger counts realized on Serbian railway network it is concluded that the time series has a strong autocorrelation of seasonal characteristics. In order to deal with seasonal periodicity, Seasonal AutoRegressive Integrated Moving Average (SARIMA) method is applied for fitting and forecasting the time series that spans over the January 2004 – June 2014 periods. Experimental results show good prediction performances. Therefore, developed SARIMA model can be considered for forecasting of monthly passenger flows on Serbian railways.
First Published Online: 7 Mar 2016
Keyword : railway, passenger service, time series, forecasting, SARIMA
How to Cite
Milenković, M., Švadlenka, L., Melichar, V., Bojović, N., & Avramović, Z. (2018). SARIMA modelling approach for railway passenger flow forecasting. Transport, 33(5), 1113-1120. https://doi.org/10.3846/16484142.2016.1139623
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Kamarianakis, Y.; Prastacos, P. 2005. Space–time modeling of traffic flow, Computers & Geosciences 31(2): 119–133. http://dx.doi.org/10.1016/j.cageo.2004.05.012
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Stephanedes, Y. J.; Michalopoulos, P. G.; Plum, R. A. 1981. Improved estimation of traffic flow for real-time control (discussion and closure), Transportation Research Record 795: 28–39.
Suhartono. 2011. Time series forecasting by using seasonal autoregressive integrated moving average: subset, multiplicative or additive model, Journal of Mathematics and Statistics 7(1): 20–27. http://dx.doi.org/10.3844/jmssp.2011.20.27
Tan, M.-C.; Wong, S. C.; Xu, J.-M.; Guan, Z.-R.; Zhang, P. 2009. An aggregation approach to short-term traffic flow prediction, IEEE Transactions on Intelligent Transportation Systems 10(1): 60–69. http://dx.doi.org/10.1109/TITS.2008.2011693
Tang, Y. F.; Lam, W. H. K.; Ng, P. L. P. 2003. Comparison of four modeling techniques for short-term AADT forecasting in Hong Kong, Journal of Transportation Engineering 129(3): 271–277. http://dx.doi.org/10.1061/(ASCE)0733-947X(2003)129:3(271)
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Vlahogianni, E. I.; Golias, J. C.; Karlaftis, M. G. 2004. Short‐term traffic forecasting: overview of objectives and meth ods, Transport Reviews 24(5): 533–557. http://dx.doi.org/10.1080/0144164042000195072
Wang, Y.; Papageorgiou, M.; Messmer, A. 2007. Real-time freeway traffic state estimation based on extended Kalman filter: a case study, Transportation Science 41(2): 167–181. http://dx.doi.org/10.1287/trsc.1070.0194
Wei, Y.; Chen, M.-C. 2012. Forecasting the short-term metro passenger flow with empirical mode decomposition and neural networks, Transportation Research Part C: Emerging Technologies 21(1): 148–162. http://dx.doi.org/10.1016/j.trc.2011.06.009
Whittaker, J.; Garside, S.; Lindvel, K. 1997. Tracking and predicting a network traffic process, International Journal of Forecasting 13(1): 51–61. http://dx.doi.org/10.1016/S0169-2070(96)00700-5
Williams, B. M. 2001. Multivariate vehicular traffic flow prediction: evaluation of ARIMAX modeling, Transportation Research Record: Journal of the Transportation Research Board 1776: 194–200. http://dx.doi.org/10.3141/1776-25
Williams, B. M.; Durvasula, P. K.; Brown, D. E. 1998. Urban Freeway traffic flow prediction: application of seasonal autoregressive integrated moving average and exponential smoothing models, Transportation Research Record 1644: 132–141. http://dx.doi.org/10.3141/1644-14
Williams, B. M.; Hoel, L. A. 2003. Modeling and forecasting vehicular traffic flow as a seasonal ARIMA process: theoretical basis and empirical results, Journal of Transportation Engineering 129(6): 664–672. http://dx.doi.org/10.1061/(ASCE)0733-947X(2003)129:6(664)
Xie, Y.; Zhang, Y. 2006. A wavelet network model for short-term traffic volume forecasting, Journal of Intelligent Transportation Systems: Technology, Planning, and Operations 10(3): 141–150. http://dx.doi.org/10.1080/15472450600798551
Xu, W.; Qin, Y.; Huang, H. 2004. A new method of railway passenger flow forecasting based on spatio-temporal data mining, in Proceedings of the 7th International IEEE Conference on Intelligent Transportation Systems, 3–6 October 2004, Washington, USA, 402–405. http://dx.doi.org/10.1109/ITSC.2004.1398932
Yaffee, R. A.; McGee, M. 2000. An Introduction to Time Series Analysis and Forecasting: with Applications of SAS and SPSS. Academic Press. 528 p.
Zhang, X.-L.; He, G.-G. 2007. Forecasting approach for short-term traffic flow based on principal component analysis and combined neural network, Systems Engineering – Theory & Practice 27(8): 167–171. http://dx.doi.org/10.1016/S1874-8651(08)60052-6
Zhang, Y.; Ye, Z. 2008. Short-term traffic flow forecasting using fuzzy logic system methods, Journal of Intelligent Transportation Systems: Technology, Planning, and Operations 12(3): 102–112. http://dx.doi.org/10.1080/15472450802262281
Box, G. E. P.; Jenkins, G. M.; Reinsel, G. C. 2013. Time Series Analysis: Forecasting and Control. John Wiley & Sons, Inc. 755 p. http://dx.doi.org/10.1002/9781118619193
Chatfield, C. 1993. Calculating interval forecasts, Journal of Business & Economic Statistics 11(2): 121–135. http://dx.doi.org/10.2307/1391361
Chen, C.-F.; Chang, Y.-H.; Chang, Y.-W. 2009. Seasonal ARIMA forecasting of inbound air travel arrivals to Taiwan, Transportmetrica 5(2): 125–140. http://dx.doi.org/10.1080/18128600802591210
Clark, S. 2003. Traffic prediction using multivariate nonparametric regression, Journal of Transportation Engineering 129(2): 161–168. http://dx.doi.org/10.1061/(ASCE)0733-947X(2003)129:2(161)
Cryer, J. D.; Chan, K.-S. 2008. Time Series Analysis: with Applications in R. Springer. 491 p. http://dx.doi.org/10.1007/978-0-387-75959-3
De Gooijer, J. G.; Abraham, B.; Gould, A.; Robinson, L. 1985. Methods for determining the order of an autoregressivemoving average process: a survey, International Statistical Review / Revue Internationale de Statistique 53(3): 301–329. http://dx.doi.org/10.2307/1402894
Dougherty, M. 1995. A review of neural networks applied to transport, Transportation Research Part C: Emerging Technologies 3(4): 247–260. http://dx.doi.org/10.1016/0968-090X(95)00009-8
Faraway, J.; Chatfield, C. 1998. Time series forecasting with neural networks: a comparative study using the air line data, Journal of the Royal Statistical Society: Series C (Applied Statistics) 47(2): 231–250. http://dx.doi.org/10.1111/1467-9876.00109
Grosche, T.; Rothlauf, F.; Heinzl, A. 2007. Gravity models for airline passenger volume estimation, Journal of Air Transport Management 13(4): 175–183. http://dx.doi.org/10.1016/j.jairtraman.2007.02.001
Grubb, H.; Mason, A. 2001. Long lead-time forecasting of UK air passengers by Holt–Winters methods with damped trend, International Journal of Forecasting 17(1): 71–82. http://dx.doi.org/10.1016/S0169-2070(00)00053-4
Hansen, J. V.; McDonald, J. B.; Nelson, R. D. 1999. Time series prediction with genetic-algorithm designed neural networks: an empirical comparison with modern statistical models, Computational Intelligence 15(3): 171–184. http://dx.doi.org/10.1111/0824-7935.00090
Kamarianakis, Y.; Prastacos, P. 2005. Space–time modeling of traffic flow, Computers & Geosciences 31(2): 119–133. http://dx.doi.org/10.1016/j.cageo.2004.05.012
Lee, S.; Fambro, D. 1999. Application of subset autoregressive integrated moving average model for short-term freeway traffic volume forecasting, Transportation Research Record 1678: 179–188. http://dx.doi.org/10.3141/1678-22
Li, H. J.; Zhang, Y.-Z.; Zhu, C.-F. 2012. Forecasting of railway passenger flow based on Grey model and monthly proportional coefficient, in 2012 IEEE Symposium on Robotics and Applications (ISRA), 3–5 June 2012, Kuala Lumpur, 23–26. http://dx.doi.org/10.1109/ISRA.2012.6219110
Lim, C.; McAleer, M. 2002. Time series forecasts of international travel demand for Australia, Tourism Management 23(4): 389–396. http://dx.doi.org/10.1016/S0261-5177(01)00098-X
Prista, N.; Diawara, N.; Costa, M. J.; Jones, C. 2011. Use of SARIMA models to assess data-poor fisheries: a case study with a sciaenid fishery off Portugal, Fishery Bulletin 109(2): 170–185.
Saab, S. S.; Zouein, P. P. 2001. Forecasting passenger load for a fixed planning horizon, Journal of Air Transport Management 7(6): 361–372. http://dx.doi.org/10.1016/S0969-6997(01)00030-8
Smith, B.; Demetsky, M. 1997. Traffic flow forecasting: comparison of modeling approaches, Journal of Transportation Engineering 123(4): 261–266. http://dx.doi.org/10.1061/(ASCE)0733-947X(1997)123:4(261)
Smith, B. L.; Williams, B. M.; Oswald, R. K. 2002. Comparison of parametric and nonparametric models for traffic flow forecasting, Transportation Research Part C: Emerging Technologies 10(4): 303–321. http://dx.doi.org/10.1016/S0968-090X(02)00009-8
Stathopoulos, A.; Karlaftis, M. G. 2003. A multivariate state space approach for urban traffic flow modeling and prediction, Transportation Research Part C: Emerging Technologies 11(2): 121–135. http://dx.doi.org/10.1016/S0968-090X(03)00004-4
Stephanedes, Y. J.; Michalopoulos, P. G.; Plum, R. A. 1981. Improved estimation of traffic flow for real-time control (discussion and closure), Transportation Research Record 795: 28–39.
Suhartono. 2011. Time series forecasting by using seasonal autoregressive integrated moving average: subset, multiplicative or additive model, Journal of Mathematics and Statistics 7(1): 20–27. http://dx.doi.org/10.3844/jmssp.2011.20.27
Tan, M.-C.; Wong, S. C.; Xu, J.-M.; Guan, Z.-R.; Zhang, P. 2009. An aggregation approach to short-term traffic flow prediction, IEEE Transactions on Intelligent Transportation Systems 10(1): 60–69. http://dx.doi.org/10.1109/TITS.2008.2011693
Tang, Y. F.; Lam, W. H. K.; Ng, P. L. P. 2003. Comparison of four modeling techniques for short-term AADT forecasting in Hong Kong, Journal of Transportation Engineering 129(3): 271–277. http://dx.doi.org/10.1061/(ASCE)0733-947X(2003)129:3(271)
Tsai, T.-H.; Lee C.-K.; Wei, C.-H. 2009. Neural network based temporal feature models for short-term railway passenger demand forecasting, Expert Systems with Applications 36(2): 3728–3736. http://dx.doi.org/10.1016/j.eswa.2008.02.071
Vlahogianni, E. I.; Golias, J. C.; Karlaftis, M. G. 2004. Short‐term traffic forecasting: overview of objectives and meth ods, Transport Reviews 24(5): 533–557. http://dx.doi.org/10.1080/0144164042000195072
Wang, Y.; Papageorgiou, M.; Messmer, A. 2007. Real-time freeway traffic state estimation based on extended Kalman filter: a case study, Transportation Science 41(2): 167–181. http://dx.doi.org/10.1287/trsc.1070.0194
Wei, Y.; Chen, M.-C. 2012. Forecasting the short-term metro passenger flow with empirical mode decomposition and neural networks, Transportation Research Part C: Emerging Technologies 21(1): 148–162. http://dx.doi.org/10.1016/j.trc.2011.06.009
Whittaker, J.; Garside, S.; Lindvel, K. 1997. Tracking and predicting a network traffic process, International Journal of Forecasting 13(1): 51–61. http://dx.doi.org/10.1016/S0169-2070(96)00700-5
Williams, B. M. 2001. Multivariate vehicular traffic flow prediction: evaluation of ARIMAX modeling, Transportation Research Record: Journal of the Transportation Research Board 1776: 194–200. http://dx.doi.org/10.3141/1776-25
Williams, B. M.; Durvasula, P. K.; Brown, D. E. 1998. Urban Freeway traffic flow prediction: application of seasonal autoregressive integrated moving average and exponential smoothing models, Transportation Research Record 1644: 132–141. http://dx.doi.org/10.3141/1644-14
Williams, B. M.; Hoel, L. A. 2003. Modeling and forecasting vehicular traffic flow as a seasonal ARIMA process: theoretical basis and empirical results, Journal of Transportation Engineering 129(6): 664–672. http://dx.doi.org/10.1061/(ASCE)0733-947X(2003)129:6(664)
Xie, Y.; Zhang, Y. 2006. A wavelet network model for short-term traffic volume forecasting, Journal of Intelligent Transportation Systems: Technology, Planning, and Operations 10(3): 141–150. http://dx.doi.org/10.1080/15472450600798551
Xu, W.; Qin, Y.; Huang, H. 2004. A new method of railway passenger flow forecasting based on spatio-temporal data mining, in Proceedings of the 7th International IEEE Conference on Intelligent Transportation Systems, 3–6 October 2004, Washington, USA, 402–405. http://dx.doi.org/10.1109/ITSC.2004.1398932
Yaffee, R. A.; McGee, M. 2000. An Introduction to Time Series Analysis and Forecasting: with Applications of SAS and SPSS. Academic Press. 528 p.
Zhang, X.-L.; He, G.-G. 2007. Forecasting approach for short-term traffic flow based on principal component analysis and combined neural network, Systems Engineering – Theory & Practice 27(8): 167–171. http://dx.doi.org/10.1016/S1874-8651(08)60052-6
Zhang, Y.; Ye, Z. 2008. Short-term traffic flow forecasting using fuzzy logic system methods, Journal of Intelligent Transportation Systems: Technology, Planning, and Operations 12(3): 102–112. http://dx.doi.org/10.1080/15472450802262281