IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v76y2015icp27-47.html
   My bibliography  Save this article

Nonlinear multivariate time–space threshold vector error correction model for short term traffic state prediction

Author

Listed:
  • Ma, Tao
  • Zhou, Zhou
  • Abdulhai, Baher

Abstract

We propose Time–Space Threshold Vector Error Correction (TS-TVEC) model for short term (hourly) traffic state prediction. The theory and method of cointegration with error correction mechanism is employed in the general design of the new statistical model TS-TVEC. An inherent connection between mathematical form of error correction model and traffic flow theory is revealed through the transformation of the well-known Fundamental Traffic Diagrams. A threshold regime switching framework is implemented to overcome any unknown structural changes in traffic time series. Spatial cross correlated information is incorporated with a piecewise linear vector error correction model. A Neural Network model is also constructed in parallel to comparatively test the effectiveness and robustness of the new statistical model. Our empirical study shows that the TS-TVEC model is an effective tool that is capable of modeling the complexity of stochastic traffic flow processes and potentially applicable to real time traffic state prediction.

Suggested Citation

  • Ma, Tao & Zhou, Zhou & Abdulhai, Baher, 2015. "Nonlinear multivariate time–space threshold vector error correction model for short term traffic state prediction," Transportation Research Part B: Methodological, Elsevier, vol. 76(C), pages 27-47.
    • Handle: RePEc:eee:transb:v:76:y:2015:i:c:p:27-47
    DOI: 10.1016/j.trb.2015.02.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261515000363
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2015.02.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    2. Gebhard Kirchgässner & Jürgen Wolters & Uwe Hassler, 2013. "Introduction to Modern Time Series Analysis," Springer Texts in Business and Economics, Springer, edition 2, number 978-3-642-33436-8, October.
    3. Hansen, Bruce E. & Seo, Byeongseon, 2002. "Testing for two-regime threshold cointegration in vector error-correction models," Journal of Econometrics, Elsevier, vol. 110(2), pages 293-318, October.
    4. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    5. Baragona, R. & Battaglia, F. & Cucina, D., 2004. "Fitting piecewise linear threshold autoregressive models by means of genetic algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 277-295, September.
    6. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part III: Multi-destination flows," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 305-313, August.
    7. Zhou Zhou, 2013. "Heteroscedasticity and Autocorrelation Robust Structural Change Detection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 726-740, June.
    8. Harold Greenberg, 1959. "An Analysis of Traffic Flow," Operations Research, INFORMS, vol. 7(1), pages 79-85, February.
    9. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part II: Queueing at freeway bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 289-303, August.
    10. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    11. repec:bla:jecsur:v:13:y:1999:i:5:p:551-76 is not listed on IDEAS
    12. Daganzo, Carlos F., 1995. "The cell transmission model, part II: Network traffic," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 79-93, April.
    13. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    14. Herrera, Juan C. & Bayen, Alexandre M., 2010. "Incorporation of Lagrangian measurements in freeway traffic state estimation," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 460-481, May.
    15. Haiqiang Chen & Terence Chong & Jushan Bai, 2012. "Theory and Applications of TAR Model with Two Threshold Variables," Econometric Reviews, Taylor & Francis Journals, vol. 31(2), pages 142-170.
    16. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    17. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    18. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    19. Wang, Yibing & Papageorgiou, Markos, 2005. "Real-time freeway traffic state estimation based on extended Kalman filter: a general approach," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 141-167, February.
    20. McLeod, A. Ian & Zhang, Ying, 2008. "Improved Subset Autoregression: With R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i02).
    21. Bruce Hansen, 1999. "Testing for Linearity," Journal of Economic Surveys, Wiley Blackwell, vol. 13(5), pages 551-576, December.
    22. Zhang, G. Peter & Qi, Min, 2005. "Neural network forecasting for seasonal and trend time series," European Journal of Operational Research, Elsevier, vol. 160(2), pages 501-514, January.
    23. Deng, Wen & Lei, Hao & Zhou, Xuesong, 2013. "Traffic state estimation and uncertainty quantification based on heterogeneous data sources: A three detector approach," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 132-157.
    24. Tao Cheng & James Haworth & Jiaqiu Wang, 2012. "Spatio-temporal autocorrelation of road network data," Journal of Geographical Systems, Springer, vol. 14(4), pages 389-413, October.
    25. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    26. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-193, January.
    27. Daganzo, Carlos F., 1994. "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 269-287, August.
    28. Treiber, Martin & Kesting, Arne & Helbing, Dirk, 2010. "Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 983-1000, September.
    29. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: Solution methods," Transportation Research Part B: Methodological, Elsevier, vol. 39(10), pages 934-950, December.
    30. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: basic theory and complex boundary conditions," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 187-196, February.
    31. Hansen,B.E., 1999. "Testing for linearity," Working papers 7, Wisconsin Madison - Social Systems.
    32. Qiao, Fengxiang & Yang, Hai & Lam, William H. K., 2001. "Intelligent simulation and prediction of traffic flow dispersion," Transportation Research Part B: Methodological, Elsevier, vol. 35(9), pages 843-863, November.
    33. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 281-287, August.
    34. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    35. Castillo, Enrique & Menéndez, José María & Sánchez-Cambronero, Santos, 2008. "Predicting traffic flow using Bayesian networks," Transportation Research Part B: Methodological, Elsevier, vol. 42(5), pages 482-509, June.
    36. Yiannis Kamarianakis & Wei Shen & Laura Wynter, 2012. "Real‐time road traffic forecasting using regime‐switching space‐time models and adaptive LASSO," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(4), pages 297-315, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ma, Tao & Zhou, Zhou & Abdulhai, Baher, 2016. "Time Series Based Hourly Traffic Flow Prediction on the GTA Freeways Using TSTVEC Model," 57th Transportation Research Forum (51st CTRF) Joint Conference, Toronto, Ontario, May 1-4, 2016 319287, Transportation Research Forum.
    2. Fang, Weiwei & Zhuo, Wenhao & Yan, Jingwen & Song, Youyi & Jiang, Dazhi & Zhou, Teng, 2022. "Attention meets long short-term memory: A deep learning network for traffic flow forecasting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    3. Ma, Tao & Zhou, Zhou & Antoniou, Constantinos, 2018. "Dynamic factor model for network traffic state forecast," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 281-317.
    4. Cai, Lingru & Zhang, Zhanchang & Yang, Junjie & Yu, Yidan & Zhou, Teng & Qin, Jing, 2019. "A noise-immune Kalman filter for short-term traffic flow forecasting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    5. Chen, Yi-Ting & Sun, Edward W. & Chang, Ming-Feng & Lin, Yi-Bing, 2021. "Pragmatic real-time logistics management with traffic IoT infrastructure: Big data predictive analytics of freight travel time for Logistics 4.0," International Journal of Production Economics, Elsevier, vol. 238(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ma, Tao & Zhou, Zhou & Antoniou, Constantinos, 2018. "Dynamic factor model for network traffic state forecast," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 281-317.
    2. Ma, Tao & Zhou, Zhou & Abdulhai, Baher, 2016. "Time Series Based Hourly Traffic Flow Prediction on the GTA Freeways Using TSTVEC Model," 57th Transportation Research Forum (51st CTRF) Joint Conference, Toronto, Ontario, May 1-4, 2016 319287, Transportation Research Forum.
    3. Himpe, Willem & Corthout, Ruben & Tampère, M.J. Chris, 2016. "An efficient iterative link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 170-190.
    4. Canepa, Edward S. & Claudel, Christian G., 2017. "Networked traffic state estimation involving mixed fixed-mobile sensor data using Hamilton-Jacobi equations," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 686-709.
    5. Costeseque, Guillaume & Lebacque, Jean-Patrick, 2014. "A variational formulation for higher order macroscopic traffic flow models: Numerical investigation," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 112-133.
    6. Bliemer, Michiel C.J. & Raadsen, Mark P.H., 2019. "Continuous-time general link transmission model with simplified fanning, Part I: Theory and link model formulation," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 442-470.
    7. Duret, Aurélien & Yuan, Yufei, 2017. "Traffic state estimation based on Eulerian and Lagrangian observations in a mesoscopic modeling framework," Transportation Research Part B: Methodological, Elsevier, vol. 101(C), pages 51-71.
    8. Ke Han & Gabriel Eve & Terry L. Friesz, 2019. "Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation," Networks and Spatial Economics, Springer, vol. 19(3), pages 869-902, September.
    9. Simoni, Michele D. & Claudel, Christian G., 2017. "A fast simulation algorithm for multiple moving bottlenecks and applications in urban freight traffic management," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 238-255.
    10. Flötteröd, G. & Osorio, C., 2017. "Stochastic network link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 180-209.
    11. Jiang, Chenming & Bhat, Chandra R. & Lam, William H.K., 2020. "A bibliometric overview of Transportation Research Part B: Methodological in the past forty years (1979–2019)," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 268-291.
    12. van Erp, Paul B.C. & Knoop, Victor L. & Hoogendoorn, Serge P., 2018. "Macroscopic traffic state estimation using relative flows from stationary and moving observers," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 281-299.
    13. Ngoduy, D. & Hoang, N.H. & Vu, H.L. & Watling, D., 2016. "Optimal queue placement in dynamic system optimum solutions for single origin-destination traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 148-169.
    14. Committee, Nobel Prize, 2003. "Time-series Econometrics: Cointegration and Autoregressive Conditional Heteroskedasticity," Nobel Prize in Economics documents 2003-1, Nobel Prize Committee.
    15. Jin, Wen-Long & Gan, Qi-Jian & Gayah, Vikash V., 2013. "A kinematic wave approach to traffic statics and dynamics in a double-ring network," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 114-131.
    16. Tumash, Liudmila & Canudas-de-Wit, Carlos & Delle Monache, Maria Laura, 2022. "Multi-directional continuous traffic model for large-scale urban networks," Transportation Research Part B: Methodological, Elsevier, vol. 158(C), pages 374-402.
    17. Raadsen, Mark P.H. & Bliemer, Michiel C.J. & Bell, Michael G.H., 2016. "An efficient and exact event-based algorithm for solving simplified first order dynamic network loading problems in continuous time," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 191-210.
    18. Xingliang Liu & Jian Wang & Tangzhi Liu & Jin Xu, 2021. "Forecasting Spatiotemporal Boundary of Emergency-Event-Based Traffic Congestion in Expressway Network Considering Highway Node Acceptance Capacity," Sustainability, MDPI, vol. 13(21), pages 1-17, November.
    19. Zheng, Zuduo & Su, Dongcai, 2016. "Traffic state estimation through compressed sensing and Markov random field," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 525-554.
    20. van der Gun, Jeroen P.T. & Pel, Adam J. & van Arem, Bart, 2017. "Extending the Link Transmission Model with non-triangular fundamental diagrams and capacity drops," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 154-178.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:76:y:2015:i:c:p:27-47. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.