Advertisement

Journal of Geographical Systems

, Volume 14, Issue 4, pp 389–413 | Cite as

Spatio-temporal autocorrelation of road network data

  • Tao Cheng
  • James Haworth
  • Jiaqiu Wang
Original Article

Abstract

Modelling autocorrelation structure among space–time observations is crucial in space–time modelling and forecasting. The aim of this research is to examine the spatio-temporal autocorrelation structure of road networks in order to determine likely requirements for building a suitable space–time forecasting model. Exploratory space–time autocorrelation analysis is carried out using journey time data collected on London’s road network. Through the use of both global and local autocorrelation measures, the autocorrelation structure of the road network is found to be dynamic and heterogeneous in both space and time. It reveals that a global measure of autocorrelation is not sufficient to explain the network structure. Dynamic and local structures must be accounted for space–time modelling and forecasting. This has broad implications for space–time modelling and network complexity.

Keywords

Spatial autocorrelation Network structure Space–time autocorrelation Space–time modelling Travel time prediction Network complexity 

JEL Classification

R41 C23 C52 

Notes

Acknowledgments

The authors would like to thank Transport for London for providing the journey time data. This research is carried out under the STANDARD project, which is sponsored by the UK Engineering and Physical Sciences Research Council under Research Grant EP/G023212/1. The support from Chinese NSF (40830530) is acknowledged. The authors are grateful to three anonymous reviewers and the editor for their valuable suggestions.

References

  1. Anselin L (1995) Local indicators of spatial association: LISA. Geogr Anal 27(2):1–25Google Scholar
  2. Black WR (1992) Network autocorrelation in transportation network and flow systems. Geogr Anal 24(3):207–222CrossRefGoogle Scholar
  3. Black WR, Thomas I (1998) Accidents on Belgium’s motorways: a network autocorrelation analysis. J Transp Geogr 6(1):23–31CrossRefGoogle Scholar
  4. Box G, Jenkins G (1970) Time series analysis: forecasting and control. Holden-Day, San FranciscoGoogle Scholar
  5. Castells M (2010) Globalisation, networking, urbanisation: reflections on the spatial dynamics of the Information Age. Urban Stud 47(13):2737–2745CrossRefGoogle Scholar
  6. Chandra S, Al-Deek H (2008) Cross-correlation analysis and multivariate prediction of spatial time series of freeway traffic speeds. Transp Res Rec 2061:64–76CrossRefGoogle Scholar
  7. Chun Y (2008) Modeling network autocorrelation within migration flows by eigenvector spatial filtering. J Geogr Syst 10(4):317–344CrossRefGoogle Scholar
  8. Cliff AD, Ord JK (1969) The problem of spatial autocorrelation. In: Scott AJ (ed) Lond Pap in Reg Sci. Pion, London, pp 25–55Google Scholar
  9. De Montis A, Caschili S, Chessa A (2011) Time evolution of complex networks: commuting systems in insular Italy. J. Geogr Syst 13(1):49–65CrossRefGoogle Scholar
  10. Ding Q, Wang X, Zhang X, Sun Z (2011) Forecasting traffic volume with space-time ARIMA model. Adv Mater Res 156–157:979–983Google Scholar
  11. Doreian P, Teuter K, Wang C (1984) Network autocorrelation models: some Monte Carlo results. Sociol Methods Res 13(2):155–200CrossRefGoogle Scholar
  12. Dougherty MS, Cobbett MR (1997) Short-term inter-urban traffic forecasts using neural networks. Int J Forecast 13(1):21–31CrossRefGoogle Scholar
  13. Dow MM (2007) Galton’s problem as multiple network autocorrelation effects: cultural trait transmission and ecological constraint. Cross-Cult Res 41(4):336–363Google Scholar
  14. Dow MM, Eff EA (2008) Global, regional, and local network autocorrelation in the standard cross-cultural sample. Cross-Cult Res 42(2):148–171CrossRefGoogle Scholar
  15. Dow MM, Burton ML, White DR, Reitz KP (1984) Galton’s problem as network autocorrelation. Am Ethnolog 11(4):754–770CrossRefGoogle Scholar
  16. Elhorst JP (2003) Specification and estimation of spatial panel data models. Int Reg Sci Rev 26(3):244–268CrossRefGoogle Scholar
  17. Farber S, Páez A, Volz E (2009) Topology and dependency tests in spatial and network autoregressive models. Geogr Anal 41(2):158–180CrossRefGoogle Scholar
  18. Flahaut B, Mouchart M, San Martin E, Thomas I (2003) The local spatial autocorrelation and the kernel method for identifying black zones: a comparative approach. Accid Anal Prev 35(6):991–1004CrossRefGoogle Scholar
  19. Florax RJGM, Rey S (1995) The impact of misspecified spatial structure in linear regression models. In: Anselin L, Florax RJGM (eds) New Dir in Spat Econom. Springer-Verlag, Berlin, pp 111–135CrossRefGoogle Scholar
  20. Geary RC (1954) The contiguity ratio and statistical mapping. Inc Stat 5(3):115–145Google Scholar
  21. Getis A, Aldstadt J (2004) Constructing the spatial weights matrix using a local statistic. Geogr Anal 36(2):90–104CrossRefGoogle Scholar
  22. Griffith DA (1996) Some guidelines for specifying the geographic weights matrix contained in spatial statistical models. In: Arlinghaus SL, Griffith DA, Drake WD, Nystuen JD (eds) Pract Handb of Spat Stat. CRC Press, Boca Raton, FL, pp 82–148Google Scholar
  23. Griffith DA (2010) Modeling spatio-temporal relationships: retrospect and prospect. J Geogr Syst 12(2):111–123CrossRefGoogle Scholar
  24. Griffith DA, Heuvelink GB (2009) Deriving space–time variograms from space–time autoregressive (STAR) model specifications. In StatGIS 2009 conference, Milos, Greece, JuneGoogle Scholar
  25. Griffith DA, Lagona F (1998) On the quality of likelihood-based estimators in spatial autoregressive models when the data dependence structure is misspecified. J Stat Plan Inference 69(1):153–174CrossRefGoogle Scholar
  26. Hackney JK, Bernard M, Bindra S, Axhausen KW (2007) Predicting road system speeds using spatial structure variables and network characteristics. J. Geogr Sys 9(4):397–417CrossRefGoogle Scholar
  27. Hardisty F, Klippel A (2010) Analysing spatio-temporal autocorrelation with LISTA-Viz. Int J Geogr Inf Sci 24(10):1515–1526CrossRefGoogle Scholar
  28. Jiang B (2007) A topological pattern of urban street networks: universality and peculiarity. Physica A 384(2):647–655CrossRefGoogle Scholar
  29. Kamarianakis Y, Prastacos P (2005) Space-time modeling of traffic flow. Comput Geosci 31(2):119–133CrossRefGoogle Scholar
  30. Leenders RT (2002) The specification of weight structures in network autocorrelation models of social influence. SOM rep ser No. 02B09Google Scholar
  31. Liu H, van Zuylen HJ, van Lint H, Salomons M (2006) Predicting urban arterial travel time with state-space neural networks and kalman filters. Transp Res Rec J Transp Res Board 1968(1):99–108CrossRefGoogle Scholar
  32. Min W, Wynter L, Amemiya Y (2007) Road traffic prediction with spatio-temporal correlations. In: Proceedings of the sixth trienn symp on transp anal, phuket Island, Thailand, June 2007Google Scholar
  33. Min X, Hu J, Chen Q, Zhang T, Zhang Y (2009) Short-term traffic flow forecasting of urban network based on dynamic STARIMA model. In: Proceedings of the 12th international IEEE conference on intelligent transportation systems, St. Louis, Missouri, USA, 3–7 Oct 2009Google Scholar
  34. Min X, Hu J, Zhang Z (2010) Urban traffic network modeling and short-term traffic flow forecasting based on GSTARIMA model. In: Proceedings of the 13th international IEEE conference on intelligent transportation systems, 19–22 Sept 2010, pp 1535–1540Google Scholar
  35. Mizruchi MS, Neuman EJ (2008) The effect of density on the level of bias in the network autocorrelation model. Soc Netw 30:190–200CrossRefGoogle Scholar
  36. Moran PAP (1950) Notes on continuous stochastic phenomena. Biometrika 37:17–23Google Scholar
  37. Neuman EJ, Mizruchi MS (2010) Structure and bias in the network autocorrelation model. Soc Netw 32(4):290–300CrossRefGoogle Scholar
  38. Newman MEJ (2003) The structure and function of complex networks. SIAM Rev 45:167–256CrossRefGoogle Scholar
  39. Olden JD, Neff BD (2001) Cross-correlation bias in lag analysis of aquatic time series. Marine Biol 138(5):1063–1070CrossRefGoogle Scholar
  40. Páez A, Scott DM, Volz E (2008) Weight matrices for social influence analysis: an investigation of measurement errors and their effect on model identification and estimation quality. Soc Netw 30(4):309–317CrossRefGoogle Scholar
  41. Patil GP (2009) Impacts and Wider Impacts on Statistics (of Cliff and Ord’s 1969 article on Spatial Autocorrelation). Geogr Anal 41(4):430–435CrossRefGoogle Scholar
  42. Peeters D, Thomas I (2009) Network autocorrelation. Geogr Anal 41(4):436–443CrossRefGoogle Scholar
  43. Pfeifer PE, Deutsch SJ (1980) A three-stage iterative procedure for space-time modelling. Technometrics 22(1):35–47CrossRefGoogle Scholar
  44. Pflieger G, Rozenblat C (2010) Introduction. Urban networks and network theory: the city as the connector of multiple networks. Urban Stud 47(13):2723–2735CrossRefGoogle Scholar
  45. Richards PI (1956) Shock waves on the highway. Oper Res 4(1):42–51CrossRefGoogle Scholar
  46. Rodgers JL, Nicewander WA (1988) Thirteen ways to look at the correlation coefficient. Am Stat 42(1):59–66CrossRefGoogle Scholar
  47. Smith BL, Williams BM, Keith Oswald R (2002) Comparison of parametric and nonparametric models for traffic flow forecasting. Transp Res Part C Emerg Technol 10(4):303–321CrossRefGoogle Scholar
  48. Soper HE, Young AW, Cave BM, Lee A, Pearson K (1917) On the distribution of the correlation coefficient in small samples. Appendix II to the papers of “Student” and R. A. Fisher. A co-operative study. Biometrika 11(4):328–413Google Scholar
  49. Stetzer F (1982) Specifying weights in spatial forecasting models: the results of some experiments. Env and Plan A 14(5):571–584CrossRefGoogle Scholar
  50. van Lint JWC, Hoogendoorn SP, van Zuylen HJ (2005) Accurate freeway travel time prediction with state-space neural networks under missing data. Transp Res Part C Emerg Technol 13(5–6):347–369CrossRefGoogle Scholar
  51. Vlahogianni EI, Golias JC, Karlaftis MG (2004) Short-term traffic forecasting: overview of objectives and methods. Transp Rev A Transnatl Transdisciplinary J 24(5):533–557Google Scholar
  52. Wang J, Cheng T, Heydecker BG, Haworth J (2010) STARIMA for journey time prediction in London. In: Heydecker BG (ed) Proceedings of the 5th IMA conference on math in transpGoogle Scholar
  53. Watts DJ, Strogatz SH (1998) Collective dynamics of “small-world” networks. Nature 393(6684):440–442CrossRefGoogle Scholar
  54. Williams BM, Hoel LA (2003) Modeling and forecasting vehicular traffic flow as a seasonal ARIMA process: theoretical basis and empirical results. J Transp Eng ASCE 129(6):664–672CrossRefGoogle Scholar
  55. Wu C, Ho J, Lee D (2004) Travel-time prediction with support vector regression. IEEE Trans Intell Transp Sys 5(4):276–281CrossRefGoogle Scholar
  56. Xie F, Levinson D (2007) Measuring the structure of road networks. Geogr Anal 39(3):336–356CrossRefGoogle Scholar
  57. Xu Z, Sui DZ (2007) Small-world characteristics on transportation networks: a perspective from network autocorrelation. J Geogr Syst 9(2):189–205CrossRefGoogle Scholar
  58. Yue Y, Yeh AGO (2008) Spatiotemporal traffic-flow dependency and short-term traffic forecasting. Environ Plan B 35(5):762–771CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Civil, Environmental and Geomatic EngineeringUniversity College LondonLondonUK

Personalised recommendations