March 2024 Network-level traffic flow prediction: Functional time series vs. functional neural network approach
Tao Ma, Fang Yao, Zhou Zhou
Author Affiliations +
Ann. Appl. Stat. 18(1): 424-444 (March 2024). DOI: 10.1214/23-AOAS1795


Traffic state prediction is an essential component and an underlying backbone of intelligent transportation systems, especially in the context of smart city framework. Its significance is mainly twofold in modern transportation systems: supporting advanced traffic operations and management for highways and urban road networks to mitigate traffic congestion and enabling individual drivers with connected vehicles in the traffic system to dynamically optimize their routes to improve travel time. Traffic state prediction with interval-based pointwise methods at 15-minute or hourly intervals is common in traffic literature. However, because traffic dynamics are a continuous process over time, the discrete-time pointwise methods for traffic prediction at a fixed time interval hardly meet the advanced demands of continuous prediction in modern transportation systems. To close the gap, we propose functional approaches to intraday and day-by-day continuous-time prediction for traffic volume. This research focuses on network-level traffic flow predictions concurrently for all locations of interest. Two functional approaches are introduced, namely, the network-integrated functional time-series model and the functional neural network model. With functional approaches a 24-hour intraday traffic profile is modeled as a functional curve over time, and sequences of historical traffic curves are used to predict traffic curves for near future days in a row and multiple locations of interest. We also include the functional varying coefficient model, Sparse VAR and traditional AR models in the comparative study; empirical results show that the network-integrated functional time-series model outperforms other approaches in terms of the accuracy of predictions at network-scale.

Funding Statement

The second author’s research was supported in part by the National Key R&D Program of China (No. 2022YFA1003801, 2020YFE0204200), the National Natural Science Foundation of China (No. 12292981, 11931001), the LMAM, the Fundamental Research Funds for the Central Universities and LMEQF.
The third author’s research was supported by the NSERC of Canada (No. 489079, 512143).


This research was to explore innovative methods for urban traffic forecasting driven by the original interest of the first author’s PhD research at the University of Toronto. The authors would like to thank the Ministry of Transportation Ontario Canada and the ITS center at the University of Toronto for traffic data. We are also thankful to the anonymous referees, the Associate Editor and the Editor for their insightful and constructive comments that improved the quality of this paper. The viewpoints expressed within the content are solely the authors’ responsibility and do not reflect the official views of any agencies.


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Tao Ma. Fang Yao. Zhou Zhou. "Network-level traffic flow prediction: Functional time series vs. functional neural network approach." Ann. Appl. Stat. 18 (1) 424 - 444, March 2024.


Received: 1 April 2022; Revised: 1 June 2023; Published: March 2024
First available in Project Euclid: 31 January 2024

Digital Object Identifier: 10.1214/23-AOAS1795

Keywords: functional neural network , functional principal component , functional time series , functional varying coefficient , Matrix-variate factor model , network-level traffic flow prediction

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 1 • March 2024
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