Technical Papers
Feb 23, 2012

Integrated Heteroscedasticity Test for Vehicular Traffic Condition Series

Publication: Journal of Transportation Engineering
Volume 138, Issue 9

Abstract

Because of the growing awareness of the importance of the traffic condition uncertainty-related studies, traffic condition uncertainty modeling is gaining increasing attention from the transportation research community. In this field, traffic condition uncertainty, gauged mainly by the conditional variance of traffic characteristics, has been investigated primarily with two major approaches, generalized autoregressive conditional heteroscedasticity approach and stochastic volatility approach; however, both lack a thorough and sound test on the applicability of these approaches. To complete this modeling gap and hence lay the theoretical basis for traffic uncertainty-related studies, an integrated heteroscedasticity test, including an optimal transformation search and four statistical tests, is proposed in this study. By using real world data collected from 36 stations across four regions in both the United Kingdom and the United States and aggregated at 15-min interval as a typical representative, the proposed integrated heteroscedasticity test is demonstrated, validating the heteroscedastic nature of the traffic conditional series. In addition, the effects of transformations are illustrated together with an online short-term traffic condition forecasting algorithm as an additional validation of this heteroscedastic nature. On firmly establishing the heteroscedastic nature of the traffic conditions, future studies are recommended to further the modeling of traffic condition uncertainties over a spectrum of time intervals and apply the uncertainty models in various applications such as travel time reliability or the proactive traffic control systems.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

The authors thank the Minnesota Department of Transportation, the Washington State Department of Transportation, and the Maryland Department of Transportation, and the United Kingdom Highways Agency for providing the traffic data used in this research. The authors hold all the responsibility on the analyses and views presented in this work. This work is supported in part by the National Science Foundation of China under the Grant No.71101025.

References

Bartlett, M. S. (1936). “The square root transformation in analysis of variance.” Suppl. J. R. Stat. Soc., 3(1), 68–78.
Bollerslev, T. (1986). “Generalized autoregressive conditional heteroscedasticity.” J. Econometrics, 31(3), 307–327.
Box, G. E. P., and Cox, D. R. (1964). “An analysis of transformations.” J. R. Stat. Soc., Ser. B, 26(2), 211–252.
Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (1994). Time series analysis: Forecasting and control, 3rd Ed., Prentice-Hall, Upper Saddle River, NJ.
Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (2008). Time series analysis: Forecasting and control, 4th Ed., Wiley, Hoboken, NJ.
Curtiss, J. T. (1943). “On transformations used in the analysis of variance.” Ann. Math. Stat., 14(2), 107–122.
Edie, L. C. (1963). “Discussion of traffic stream measurements and definitions.” Proc., 2nd Int. Symp. on the Theory of Traffic Flow, Almond, J.ed., 139–154, Organisation for Economic Cooperation and Development (OECD), Paris.
Engle, R. F. (1982). “Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation.” Econometrica, 50(4), 987–1008.
Finney, D. J. (1941). “On the distribution of a variate whose logarithm is normally distributed.” Suppl. J. R. Stat. Soc., 7(2), 155–161.
Foi, A. (2009). “Optimization of variance-stabilizing transformations.” 〈http://www.cs.tut.fi/~foi/〉 (May 2011).
Fuller, W. A. (1996). Introduction to statistical time series, 2nd Ed., Wiley, Hoboken, NJ.
Guo, J. (2005). “Adaptive estimation and prediction of univariate traffic condition series.” Ph.D. dissertation, North Carolina State Univ., Raleigh, NC.
Guo, J., and Williams, B. M. (2010). “Real time short term traffic speed level forecasting and uncertainty quantification using layered Kalman filters.”, Transportation Research Board, Washington, DC, 28–37.
Guo, J., Williams, B. M., and Smith, B. L. (2008). “Study of data collection time intervals for stochastic short-term traffic flow forecasting.”, Transportation Research Board, Washington, DC, 18–26.
Kamarianakis, Y., Kanas, A., and Prastacos, P. (2005). “Modeling traffic volatility dynamics in an urban network.”, Transportation Research Board, Washington, DC, 18–27.
Laurent, S., and Peters, J. P. (2002). “G@RCH 2.2: An ox package for estimating and forecasting various arch models.” J. Econ. Surv., 16(3), 447–485.
SAS Institute, Inc. (2000). SAS OnlineDoc, Version 8, SAS Institute, Cary, NC.
Smith, B. L., Schere, W. T., and Conklin, J. H. (2003). “Exploring imputation techniques for missing data in transportation management systems.”, Transportation Research Board, Washington, DC, 132–142.
Smith, B. L., Williams, B. M., and Oswald, R. K. (2002). “Comparison of parametric and nonparametric models for traffic flow forecasting.” Transp. Res. Part C, 10(4), 303–321.
Sohn, K., and Kim, D. (2009). “Statistical model for forecasting link travel time variability.” J. Trans. Eng., 135(7), 440–453.
Steel, R. G. D., Torrie, J. H., and Dickey, D. A. (1997). Principles and procedures of statistics: A biometrical approach, McGraw-Hill, New York.
Tsekeris, T., and Stathopoulos, A. (2006). “Real-time traffic volatility forecasting in urban arterial networks.”, Transportation Research Board, Washington, DC, 146–156.
Tsekeris, T., and Stathopoulos, A. (2010). “Short-term prediction of urban traffic variability: Stochastic volatility modeling approach.” J. Trans. Eng., 136(7), 606–613.
Williams, B. M. (1999). “Modeling and forecasting vehicular traffic flow as a seasonal stochastic time series process.” Ph.D. dissertation, Univ. of Virginia, Charlottesville, VA.
Williams, B. M., and Hoel, L. A. (2003). “Modeling and forecasting vehicular traffic flow as a seasonal ARIMA: Theoretical basis and empirical results.” J. Trans. Eng., 129(6), 664–672.
Yang, M., Liu, Y., and You, Z. (2010). “The reliability of travel time forecasting.” IEEE Trans. Intell. Trans. Syst., 11(1), 162–171.

Information & Authors

Information

Published In

Go to Journal of Transportation Engineering
Journal of Transportation Engineering
Volume 138Issue 9September 2012
Pages: 1161 - 1170

History

Received: Jul 28, 2011
Accepted: Feb 22, 2012
Published online: Feb 23, 2012
Published in print: Sep 1, 2012

Permissions

Request permissions for this article.

Authors

Affiliations

Jianhua Guo [email protected]
Professor, Intelligent Transportation System Research Center, Southeast Univ., Si Pai Lou #2, Nanjing, P.R. China 210096 (corresponding author). E-mail: [email protected]
Professor, Intelligent Transportation System Research Center, Southeast Univ., Si Pai Lou #2, Nanjing, P.R. China 210096. E-mail: [email protected]
Billy M. Williams [email protected]
Associate Professor, Dept. of Civil, Construction, and Environmental Engineering, North Carolina State Univ., Raleigh, NC 27695. E-mail: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share