Forecasting Traffic Speed Based on Spatiotemporal Dependencies: A Sarimax Modeling Framework

Accurate traffic prediction can assist path planning, guide vehicle scheduling and alleviate traffic congestion. In this paper we propose a seasonal autoregressive integrated moving average model with exogenous variables and interaction variables to forecast road segment speed of complex urban road networks, in which the dynamic space-time dependent information of urban road networks is utilized. First, traffic information about spatial and temporal features from upstream intersections is fed into the model through two variable selections and divided into weekday and non-weekday modes. Then, the proposed method is compared with traditional time series methods and a deep learning-based method, Long Short-Term Memory (LSTM). Finally, we use the Ljung-Box test to check the randomness of the residuals and the significance of the model. The results show that the multivariate SARIMAX model with spatio-temporal interactions has a better performance than compared methods in terms of accuracy and residual results. The root mean square error (RMSE) of our model  is 0.62, and the mean absolute percentage error (MAPE) is 3.20, and the residuals of the 10 roads we studied are all white noise. The proposed method can capture useful information from data and improves prediction accuracy effectively.