Adaptive Estimation and Prediction of Univariate Vehicular Traffic Condition Series

Aimed at providing the anticipatory ability for the proactive traffic control systems, a new adaptive online short-term univariate traffic condition forecasting method is presented in this dissertation by assimilating knowledge from previous research. Using 15-minute traffic flow series as a representative, this methodology is based on the hypothesis that the first two conditional moments of univariate traffic flow series can be modeled as a SARIMA+GARCH structure, based on which an online forecasting system can be developed using seasonal exponential smoothing and Kalman filter. Supplementary components, including missing value imputation and outlier detection, can be incorporated into the system to meet the requirements of real traffic data collection situations.The development of the system follows two steps. In step (1), the SARIMA model is separated into a seasonal component handling traffic flow level due to historical traffic information, and a short-term component handling local variation after the traffic level due to historical information is subtracted. The seasonal component is processed using seasonal exponential smoothing by recognizing the theoretical equivalence between ARIMA model and exponential smoothing; the local variation is processed using Kalman filter by constructing a state space model. Afterwards, GARCH model is processed using Kalman filter based on the recognition that GARCH has an equivalent representation as ARMA in the sense of squared series. In step (2), missing values are replaced with one-step-ahead forecasts, and the system will not be updated since missing values convey no information. Outliers, indicating extraordinary patterns, are detected based on intervention analysis and likelihood ratio test. Outliers are proved to be assimilated into the system through an investigation showing outliers do have significant influences on the forecasting system. Additionally, the square root transformation is applied in the system.Using real traffic operation data from four regions, the research hypothesis is validated and the proposed methodology is implemented and proved to bear desirable attributes, including competencies, adaptability, computational efficiency, robustness, and transferability.