This article presents the theoretical basis for modeling univariate traffic condition data streams as seasonal autoregressive integrated moving average processes. This foundation rests on the Wold decomposition theorem and on the assertion that a one-week lagged first seasonal difference applied to discrete interval traffic condition data will yield a weakly stationary transformation. Moreover, empirical results using actual intelligent transportation system data are presented and found to be consistent with the theoretical hypothesis. Conclusions are given on the implications of these assertions and findings relative to ongoing intelligent transportation systems research, deployment, and operations.

The application of seasonal time series models to the single-interval traffic flow forecasting problem for urban freeways is addressed. Seasonal time series approaches have not been used in previous forecasting research. However, time series of traffic flow data are characterized by definite periodic cycles. Seasonal autoregressive integrated moving average (ARIMA) and Winters exponential smoothing models were developed and tested on data sets belonging to two sites: Telegraph Road and the Woodrow Wilson Bridge on the inner and outer loops of the Capital Beltway in northern Virginia. Data were 15-min flow rates and were the same as used in prior forecasting research by B. Smith. Direct comparisons with the Smith report findings were made and it was found that ARIMA (2, 0, 1)(0, 1, 1)₉₆ and ARIMA (1, 0, 1)(0, 1, 1)₉₆ were the best-fit models for the Telegraph Road and Wilson Bridge sites, respectively. Best-fit Winters exponential smoothing models were also developed for each site. The single-step forecasting results indicate that seasonal ARIMA models outperform the nearest-neighbor, neural network, and historical average models as reported by Smith.

Short-term freeway traffic flow forecasting efforts to date have focused on predictions based solely on previous observations at the location of interest. This univariate prediction is useful for certain types of intelligent transportation system (ITS) forecasts, such as operational demand forecasts at system entry points. In addition, data from upstream sensors should improve forecasts at downstream locations. This motivates investigation of multivariate forecast models that include upstream sensor data. A candidate model is transfer functions with autoregressive integrated moving average errors, otherwise known as the ARIMAX model. The ARIMAX model was applied to motorway data from France that had been the subject of previous traffic flow forecasting research. The results indicate that ARIMAX models provide improved forecast performance over univariate forecast models. However, several issues must be addressed before widespread use of ARIMAX models for ITS forecasts is feasible. These issues include the increased complexity of model specification, estimation, and maintenance; model consistency; model robustness in the face of interruptions in the upstream data series; and variability in the cross-correlation between upstream and downstream observations. The last issue is critical because ARIMAX models assume constant transfer function parameters, whereas the correlation between upstream and downstream observations vary with prevailing traffic conditions, especially traffic stream speed. Therefore, further research is needed to investigate model extensions and refinements to provide a generalizable, self-tuning multivariate forecasting model that is easily implemented and that effectively models varying upstream to downstream correlations.

Conventionally, most traffic forecasting models have been applied in a static framework in which new observations are not used to update model parameters automatically. The need to perform periodic parameter reestimation at each forecast location is a major disadvantage of such models. From a practical standpoint, the usefulness of any model depends not only on its accuracy but also on its ease of implementation and maintenance. This paper presents an adaptive parameter estimation methodology for univariate traffic condition forecasting through use of three well-known filtering techniques: the Kalman filter, recursive least squares, and least mean squares. Results show that forecasts obtained from recursive adaptive filtering methods are comparable with those from maximum likelihood estimated models. The adaptive methods deliver this performance at a significantly lower computational cost. As recursive, self-tuning predictors, the adaptive filters offer plug-and-play capability ideal for implementation in real-time management and control systems. The investigation presented in this paper also demonstrates the robustness and stability of the seasonal time series model underlying the adaptive filtering techniques.