A Nonlinear Autoregressive Model with Exogenous Variables for Traffic Flow Forecasting in Smaller Urban Regions

Li, Junzhuo; Li, Wenyong; Lian, Guan · 2022 · DOAJ

DOI: 10.7307/ptt.v34i6.4145

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Summary

This paper addresses the challenge of accurate short-term traffic flow forecasting in smaller urban regions, where data-driven methods often fail due to insufficient training data, complex calculations, and poor portability. While traditional model-driven approaches like ARIMA require strict statistical assumptions that traffic data often violates, and modern deep learning models like LSTM require large datasets and significant computational resources, smaller cities typically possess sparse, low-density traffic data. To bridge this gap, the authors propose a Nonlinear AutoRegressive model with eXogenous variables (NARX) that utilizes a Focused Time-Delay Neural Network (FTDNN) as its nonlinear function. This approach aims to capture the nonlinear dynamics of traffic flow while maintaining a simple structure that requires less data and computational power than complex recurrent neural networks. The methodology employs an FTDNN with a Tapped Delay Line (TDL) structure to provide short-term memory capabilities without the gating mechanisms found in LSTM or RNN models, thereby reducing parameter complexity. The NARX model is trained using a series-parallel structure and predicts using a parallel structure. To address long-term correlations and daily traffic trends, the study incorporates trend decomposition via dummy variables and difference calculation methods on the time series. The experimental validation uses traffic flow data collected from four detection points on North Zhongshan Road in Guilin, China, over four days (April 6–10, 2020). The data, sampled every five minutes, includes speed, density, occupancy rate, and traffic flow. The performance of the proposed NARX-FTDNN model is compared against Seasonal ARIMA (SARIMA) and Holt-Winters models. The results demonstrate that the NARX model with FTDNN outperforms both SARIMA and Holt-Winters in forecasting accuracy for five-minute intervals. The analysis highlights that the FTDNN structure is particularly advantageous for small-city scenarios characterized by short sequence lengths and small feature sizes, as it requires significantly fewer parameters than equivalent RNN models. For instance, with 64 hidden units, the FTDNN required only 1,600 parameters compared to 5,440 for an RNN. The integration of difference calculations and dummy variables effectively captured the deterministic daily trends of traffic flow, enhancing the model's predictive capability despite the limited data volume. The significance of this work lies in providing a practical, computationally efficient solution for Intelligent Transportation Systems in smaller urban areas. By avoiding the data hunger and complexity of deep learning models and the rigid assumptions of linear statistical models, the NARX-FTDNN approach offers a robust alternative for traffic management. It enables accurate short-term forecasting with minimal data requirements, facilitating better traffic policy formulation and congestion alleviation in cities where large-scale data collection infrastructure is lacking.

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