Investigation of temporal freeway traffic patterns in reconstructed state spaces

Abarbanel, 1996 Ansley, 1977, On the structure of moving average processes, Journal Econometrics, 6, 121, 10.1016/0304-4076(77)90058-6 Box, G.E.P., Hillmer, S.C., Tiao, G.C., 1976. Analysis and modeling of seasonal time series. N.B.E.R. – Census Conference on Seasonal Time Series, Washington, DC. Chang, 1999, Real-time prediction of traffic flows using dynamic generalized linear models, Transportation Research Record, 1678, 168, 10.3141/1678-21 Clarke, 1983, An algorithm for testing goodness of fit of ARMA (P,Q) models, Applied Statistics, 32, 335, 10.2307/2347966 Dendrinos, 1994, Traffic-flow dynamics: a search for chaos, Chaos, Solitons & Fractals, 4, 605, 10.1016/0960-0779(94)90069-8 Disbro, 1989, Traffic flow theory and chaotic behavior, Transportation Research Record, 1225, 109 Fraser, 1986, Independent coordinates for strange attractors from mutual information, Physical Review A, 33, 1134, 10.1103/PhysRevA.33.1134 Grassberger, 1983, Measuring the strangeness of strange attractors, Physica D, 9, 189, 10.1016/0167-2789(83)90298-1 Hilborn, 2000 Jenkins, 1981, Some aspects of modeling and forecasting multivariate time series, Journal of Time Series Analysis, 2, 1, 10.1111/j.1467-9892.1981.tb00309.x Kants, 2004 Kennel, 1992, Determining embedding dimension for phase-space reconstruction using a geometrical construction, Physical Review A, 45, 3403, 10.1103/PhysRevA.45.3403 Kerner, B.S., 1998. A Theory of Congested Traffic Flow. In: Proceedings of the 3rd Symposium on Highway Capacity and Level of Service 2, pp. 621–642. Kerner, 1999, Congested traffic flow: observations and theory, Transportation Research Record, 1678, 160, 10.3141/1678-20 Kerner, 2002, Synchronized flow as a new traffic phase and related problems for traffic flow modeling, Mathematical and Computer Modeling, 35, 481, 10.1016/S0895-7177(02)80017-6 Kerner, 2002, Empirical macroscopic features of spatial–temporal traffic patterns at highway bottlenecks, Physical Review E, 65, 046138, 10.1103/PhysRevE.65.046138 Kerner, 2004 Kerner, 2002, A microscopic model for phase transitions in traffic flow, Journal of Physics A: Mathematical and General, 35, L31, 10.1088/0305-4470/35/3/102 Kerner, 2002, A cellular automata approach to three-phase traffic theory, Journal of Physics A: Mathematical and General, 35, 9971, 10.1088/0305-4470/35/47/303 Kerner, 2004, Recognition and tracking of spatial–temporal congested traffic patterns on freeways, Transportation Research Part C, 12, 369, 10.1016/j.trc.2004.07.015 Kerner, 2006, Criterion for traffic phase in single vehicle data and empirical text of three-phase traffic theory, Journal of Physics A: Mathematical and General, 39, 2001, 10.1088/0305-4470/39/9/002 Lan, 2003, Testing and prediction of traffic flow dynamics with chaos, Journal of the Eastern Asia Society for Transportation Studies, 5, 1975 Lee, 1999, Application of subset autoregressive integrated moving average model for short-term freeway traffic volume forecasting, Transportation Research Record, 1678, 179, 10.3141/1678-22 Lingras, 2000, Traffic volume time-series analysis according to the type of road use, Computer-Aided Civil and Infrastructure Engineering, 15, 365, 10.1111/0885-9507.00200 Liu, 1991, Forecasting residential consumption of natural gas using monthly and quarterly time series, International Journal of Forecasting, 7, 3, 10.1016/0169-2070(91)90028-T Maravall, 1983, An application of nonlinear time series forecasting, Journal Business Economic Statistics, 1, 66, 10.2307/1391774 May, 1990 Nayfeh, 1995 Shang, 2005, Chaotic analysis of traffic time series, Chaos, Solitons & Fractal, 25, 121, 10.1016/j.chaos.2004.09.104 Sheu, 2004, Stochastic modeling and real-time prediction of incident effects on surface street traffic congestion, Applied Mathematical Modelling, 28, 445, 10.1016/j.apm.2003.10.004 Smith, 2002, Comparison of parametric and nonparametric models for traffic flow forecasting, Transportation Research Part C, 10, 303, 10.1016/S0968-090X(02)00009-8 Stathopoulos, 2003, A multivariate state space approach for urban traffic flow modeling and prediction, Transportation Research Part C, 11, 121, 10.1016/S0968-090X(03)00004-4 Takens, 1981, vol. 898 Varaiya, 2005, What we’ve learned about highway congestion, Access, 27, 2 Williams, B.M., 2001. Multivariate vehicular traffic flow prediction: an evaluation of ARIMAX modeling. In: Transportation Research Board Annual Meeting, Washington, DC, pp. 194–200. Williams, 2003, Modeling and forecasting vehicular traffic flow as a seasonal ARIMA process: theoretical basis and empirical results, Journal of Transportation Engineering, 129, 664, 10.1061/(ASCE)0733-947X(2003)129:6(664) Zhang, 1998, Chaos in a dynamic model of traffic flows in an origin–destination network, Chaos, 8, 503, 10.1063/1.166331