Adaptive Kalman filter approach for stochastic short-term traffic flow rate prediction and uncertainty quantification

• Short-term traffic forecasting includes point forecasts and interval forecasts.
• Traffic flow series can be modeled as SARIMA + GARCH process.
• SARIMA + GARCH process can be processed recursively by Kalman filters.
• Adaptive Kalman filter can enhance Kalman filter through process variance update.

Short term traffic flow forecasting has received sustained attention for its ability to provide the anticipatory traffic condition required for proactive traffic control and management. Recently, a stochastic seasonal autoregressive integrated moving average plus generalized autoregressive conditional heteroscedasticity (SARIMA + GARCH) process has gained increasing notice for its ability to jointly generate traffic flow level prediction and associated prediction interval. Considering the need for real time processing, Kalman filters have been utilized to implement this SARIMA + GARCH structure. Since conventional Kalman filters assume constant process variances, adaptive Kalman filters that can update the process variances are investigated in this paper. Empirical comparisons using real world traffic flow data aggregated at 15-min interval showed that the adaptive Kalman filter approach can generate workable level forecasts and prediction intervals; in particular, the adaptive Kalman filter approach demonstrates improved adaptability when traffic is highly volatile. Sensitivity analyses show that the performance of the adaptive Kalman filter stabilizes with the increase of its memory size. Remarks are provided on improving the performance of short term traffic flow forecasting.