Functional Time Series Modeling of Traffic Flow: A Probabilistic Approach to Temporal Symmetry

Reliable short-term traffic flow prediction is crucial for intelligent transportation systems to enable real-time control, mitigate congestion, and improve urban mobility. However, traffic dynamics are inherently uncertain, temporally dependent, and subject to pronounced intraday variability, making accurate forecasting challenging. To address these issues, this study introduces a Functional AutoRegressive (FAR) model that represents daily traffic profiles as continuous stochastic functions rather than discrete observations, thereby preserving temporal continuity and capturing underlying symmetric structures. The model is developed using high-frequency traffic data collected at 15-min intervals from the Dublin Airport Link Road, Ireland, covering January 2022 to December 2024; data from 2022–2023 are used for model estimation, while 2024 data are reserved for one-day-ahead out-of-sample evaluation. A moving-window filtering technique is incorporated to enhance robustness by probabilistically identifying outliers and reducing noise. The proposed FAR approach is benchmarked against conventional models, including autoregressive (AR), autoregressive moving average (ARMA), nonparametric autoregressive (NPAR), and vector autoregressive (VAR) models. Empirical results demonstrate that the FAR model consistently achieves superior forecasting performance across all traffic conditions, yielding a full-day MAPE of 9.160% compared to 11.623% for the VAR model, along with lower MAE (76.772) and RMSE (131.767). It also performs best on both workdays and weekends, with MAPEs of 8.129% and 10.438%, respectively. Moreover, the model remains robust across peak and off-peak periods, effectively capturing both symmetric and asymmetric traffic variations while offering a more interpretable representation of intraday patterns. These findings suggest that functional time series modeling provides an effective and computationally efficient framework for traffic forecasting, with strong potential for application in next-generation intelligent transportation systems.