Temporal aggregation in traffic data: implications for statistical characteristics and model choice

Abstract Time series techniques are useful for analyzing transportation data, uncovering past trends and providing projections. Such analyses are sensitive to the temporal aggregation of the data, an issue that has been widely ignored in the transportation literature. In traffic engineering, aggregation usually equals to the average of a variable across large regular time intervals, such as 15 minutes, hours, days, months and so on. We investigate the effects of temporal aggregation on time series of traffic volume and occupancy in urban signalized arterials. Results indicate that aggregation eliminates long memory characteristics and variance heterogeneity; this leads to smoothing traffic variation and creating a time series structure that has reduced sensitivity to changes in traffic. Moreover, aggregation was found to directly affect volatility as captured by the parameters of the Generalized Auto-Regressive Conditionally Heteroskedastic (GARCH) models.

[1]  Fengxiang Qiao,et al.  Double-Sided Determination of Aggregation Level for Intelligent Transportation System Data , 2004 .

[2]  Menghan Liu,et al.  Double-Sided Optimization of ITS Data Aggregation Via Wavelet Transformation , 2008 .

[3]  P. Perron,et al.  Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power , 2001 .

[4]  P. Phillips,et al.  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? , 1992 .

[5]  Timothy C. Coburn,et al.  Statistical and Econometric Methods for Transportation Data Analysis , 2004, Technometrics.

[6]  Alexander Skabardonis,et al.  Statistical characteristics of transitional queue conditions in signalized arterials , 2007 .

[7]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[8]  A. I. McLeod,et al.  Preservation of the rescaled adjusted range: 1. A reassessment of the Hurst Phenomenon , 1978 .

[9]  Yiannis Kamarianakis,et al.  Modeling Traffic Volatility Dynamics in an Urban Network , 2005 .

[10]  Matthew G. Karlaftis,et al.  Spectral and cross-spectral analysis of urban traffic flows , 2001, ITSC 2001. 2001 IEEE Intelligent Transportation Systems. Proceedings (Cat. No.01TH8585).

[11]  J. Durbin,et al.  Techniques for Testing the Constancy of Regression Relationships Over Time , 1975 .

[12]  Eleni I. Vlahogianni,et al.  Enhancing Predictions in Signalized Arterials with Information on Short-Term Traffic Flow Dynamics , 2009, J. Intell. Transp. Syst..

[13]  Pierre Perron,et al.  THE LIMIT DISTRIBUTION OF THE CUSUM OF SQUARES TEST UNDER GENERAL MIXING CONDITIONS , 2008, Econometric Theory.

[14]  Baher Abdulhai,et al.  Short-Term Traffic Flow Prediction Using Neuro-Genetic Algorithms , 2002, J. Intell. Transp. Syst..

[15]  Cheol Oh,et al.  Exploring the Relationship between Data Aggregation and Predictability to Provide Better Predictive Traffic Information , 2005 .

[16]  Fengxiang Qiao,et al.  Optimizing Aggregation Level for Intelligent Transportation System Data Based on Wavelet Decomposition , 2003 .

[17]  Simon Washington,et al.  Statistical and Econometric Methods for Transportation Data Analysis (2nd Edition) , 2010 .

[18]  K. Hadri.  Testing The Null Hypothesis Of Stationarity Against The Alternative Of A Unit Root In Panel Data With Serially Correlated Errors , 1999 .

[19]  P.H.A.J.M. van Gelder,et al.  Detecting long-memory: Monte Carlo simulations and application to daily streamflow processes , 2006 .

[20]  J. Geweke,et al.  THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS , 1983 .

[21]  R. Baillie,et al.  Fractionally integrated generalized autoregressive conditional heteroskedasticity , 1996 .

[22]  C. Granger.  Investigating Causal Relations by Econometric Models and Cross-Spectral Methods , 1969 .

[23]  Antony Stathopoulos,et al.  Real-Time Traffic Volatility Forecasting in Urban Arterial Networks , 2006 .

[24]  Ying-Wong Cheung,et al.  TESTS FOR FRACTIONAL INTEGRATION: A MONTE CARLO INVESTIGATION , 1993 .

[25]  C. Granger,et al.  AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING , 1980 .

[26]  Susan Grant-Muller,et al.  Use of sequential learning for short-term traffic flow forecasting , 2001 .

[27]  James H Banks.  Investigation of Some Characteristics of Congested Flow , 1999 .

[28]  Tadashi Ugaheri.  On a limit distribution , 1949 .

[29]  Brian Lee Smith,et al.  Data Collection Time Intervals for Stochastic Short-Term Traffic Flow Forecasting , 2007 .

[30]  Byron J. Gajewski,et al.  Intelligent Transportation System Data Archiving: Statistical Techniques for Determining Optimal Aggregation Widths for Inductive Loop Detector Speed Data , 2000 .

[31]  Matthew G. Karlaftis,et al.  A multivariate state space approach for urban traffic flow modeling and prediction , 2003 .

[32]  Eleni I. Vlahogianni,et al.  Temporal Evolution of Short‐Term Urban Traffic Flow: A Nonlinear Dynamics Approach , 2008, Comput. Aided Civ. Infrastructure Eng..

[33]  Billy M. Williams,et al.  Modeling and Forecasting Vehicular Traffic Flow as a Seasonal ARIMA Process: Theoretical Basis and Empirical Results , 2003, Journal of Transportation Engineering.

[34]  Mitsuhiro Odaki.  On the invertibility of fractionally differenced ARIMA processes , 1993 .

[35]  Eleni I. Vlahogianni,et al.  Optimized and meta-optimized neural networks for short-term traffic flow prediction: A genetic approach , 2005 .

[36]  Mecit Cetin,et al.  Short-Term Traffic Flow Prediction with Regime Switching Models , 2006 .

[37]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[38]  Y. Kamarianakis,et al.  Forecasting Traffic Flow Conditions in an Urban Network: Comparison of Multivariate and Univariate Approaches , 2003 .

[39]  Eleni I. Vlahogianni,et al.  Statistical methods for detecting nonlinearity and non-stationarity in univariate short-term time-series of traffic volume , 2006 .

[40]  Doug Robertson,et al.  Study of Speed-Flow Relationships on Individual Freeway Lanes , 1997 .

[41]  J. Cramer,et al.  EFFICIENT GROUPING, REGRESSION AND CORRELATION IN ENGEL CURVE ANALYSIS* , 1964 .

[42]  Brian L. Smith,et al.  Freeway Traffic flow rate measurement: Investigation into impact of measurement time interval , 2003 .

[43]  Paul Turner,et al.  Power properties of the CUSUM and CUSUMSQ tests for parameter instability , 2010 .

[44]  Thomas L. Burr,et al.  Modeling Financial Time Series With S—Plus , 2007, Technometrics.

[45]  Eleni I. Vlahogianni,et al.  Memory properties and fractional integration in transportation time-series , 2009 .

[46]  Arnold Zellner,et al.  A Study of Some Aspects of Temporal Aggregation Problems in Econometric Analyses , 1971 .

[47]  Eleni I. Vlahogianni,et al.  Short‐term traffic forecasting: Overview of objectives and methods , 2004 .

[48]  H. Akaike.  A new look at the statistical model identification , 1974 .

[49]  Mark Dougherty,et al.  SHORT TERM INTER-URBAN TRAFFIC FORECASTS USING NEURAL NETWORKS , 1997 .

[50]  P. Whittle,et al.  Estimation and information in stationary time series , 1953 .

[51]  John J. Seater,et al.  Temporal Aggregation and Economic Time Series , 1995 .

[52]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .