Modeling and Forecasting Vehicular Traffic Flow as a Seasonal ARIMA Process: Theoretical Basis and Empirical Results

By Billy M. Williams, L. Hoel. Journal of transportation engineering, 2003

1,808 citations recorded by the source corpus.

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.

Subfields: Building and Construction, Management Science and Operations Research, Transportation

View Paper: https://www.semanticscholar.org/paper/356052cf65e3aba8cc3191d11757fc802cd67eea

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Citations in the corpus

Learning Dynamics and Heterogeneity of Spatial-Temporal Graph Data for Traffic Forecasting (2021, background): “Therefore, it is natural to adapt the classic time series analysis models for the trafﬁc forecasting problem in the earlier days, and the representatives include Auto-Regres-sive Integrated Moving Average (ARIMA) [1], and Vector Auto-Regressive (VAR) [2].”
Attention Based Spatial-Temporal Graph Convolutional Networks for Traffic Flow Forecasting (2019, methodology): “The statistical models used for trafﬁc prediction include HA, ARIMA (Williams and Hoel 2003), VAR (Zivot and Wang 2006), etc.”
Decoupled Dynamic Spatial-Temporal Graph Neural Network for Traffic Forecasting (2022, neutral): “, single variant time series) prediction task [20] and address it via various conventional statistic-based methods, such as auto-regressive integrated moving average (ARIMA [38]) and Kalman filtering [18].”
Short-term traffic flow prediction based on spatio-temporal analysis and CNN deep learning (2019, methodology): “Seasonal ARIMA ( p, d, q ) ( P, D, Q )s model was employed in this paper (Williams and Hoel 2003) and the Akaike Information Criterion (AIC) is used to determine the appropriate order of ARIMA.”
Predictions of Freeway Traffic Speeds and Volumes Using Vector Autoregressive Models (2009, methodology): “Williams and Hoel (2003) also used SARIMA to forecast 15-minute traffic flows on two freeways and compared it with naı̈ve benchmark forecasts from random walk forecasts and historical averages and concluded that the parsimonious three-parameter SARIMA model with one-week differencing lag should be…”
Forecasting the short-term metro passenger flow with empirical mode decomposition and neural networks (2012, methodology): “In addition, with the characteristics of seasonality and trends in traffic data, some researchers have applied seasonal ARIMA to predict traffic flow (Williams and Hoel, 2003; .”
Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting (2021, methodology): “Classic methods, including autoregressive integrated moving average (ARIMA), k-nearest neighbors algorithm (kNN), and support vector machine (SVM), can only take temporal information into account, without considering spatial features.[14, 28, 29].”
Dynamic Spatial-Temporal Graph Convolutional Neural Networks for Traffic Forecasting (2019, positive): “Some studies apply traditional machine learning methods, such as auto-regressive and moving average model (ARMA) (Williams and Hoel 2003) and support vector regression (SVR) (Chen et al. 2015) and etc, to forecast future traffic.”
A novel wavelet-SVM short-time passenger flow prediction in Beijing subway system (2015, methodology): “Because the approximate daily-periodic trend of original passenger flow data may influence the prediction, a lot of researchers [35,74,75,19,76] have proposed various methods to remove this trend in order to improve the forecasting results, and make the prediction on the residual time series.”
Short-term traffic flow prediction using seasonal ARIMA model with limited input data (2015, methodology): “More than 2 months of traffic volume observations was used by Williams and Hoel [23] and around 60, 000 flow observations aggregated for each 3 min. intervals spanned over a period of 106 days was used by Stathopoulos and Karlaftis [30].”
Deep Learning on Traffic Prediction: Methods, Analysis, and Future Directions (2021, methodology): “In time-series analysis, autoregressive integrated moving average (ARIMA) [11] and its variants are one of the most consolidated approaches based on classical statistics and have”
Spatial-Temporal Synchronous Graph Convolutional Networks: A New Framework for Spatial-Temporal Network Data Forecasting (2020, methodology): “Many of classic methods like ARIMA (Williams and Hoel 2003) and SVM (Drucker et al.”
A Survey on Modern Deep Neural Network for Traffic Prediction: Trends, Methods and Challenges (2020, methodology): “Hoel [19] applied Seasonal ARIMA to the United States and the United King-”
An Aggregation Approach to Short-Term Traffic Flow Prediction (2009, methodology): “As the MA and ES models cannot handle trend or seasonality well [31] and the ARIMA model is often used to forecast hourly time series [6], [7], we use the ARIMA model to forecast time series s3(t).”