Deep learning models for traffic forecasting often assume the residual is independent and isotropic across time and space. This assumption simplifies loss functions such as mean absolute error, but real-world residual processes often exhibit significant autocorrelation and structured spatiotemporal correlation. This paper introduces a dynamic regression (DR) framework to enhance existing spatiotemporal traffic forecasting models by incorporating structured learning for the residual process. We assume the residual of the base model (i.e., a well-developed traffic forecasting model) follows a matrix-variate seasonal autoregressive (AR) model, which is seamlessly integrated into the training process through the redesign of the loss function. Importantly, the parameters of the DR framework are jointly optimized alongside the base model. We evaluate the effectiveness of the proposed framework on state-of-the-art (SOTA) deep traffic forecasting models using both speed and flow datasets, demonstrating improved performance and providing interpretable AR coefficients and spatiotemporal covariance matrices.

翻译：用于交通预测的深度学习模型通常假设残差在时间和空间上独立且各向同性。这一假设简化了诸如平均绝对误差等损失函数，但现实世界中的残差过程常表现出显著的自相关和结构化的时空相关性。本文引入了一种动态回归框架，通过纳入对残差过程的结构化学习，以增强现有的时空交通预测模型。我们假设基础模型（即一个成熟的交通预测模型）的残差服从矩阵变量季节性自回归模型，该模型通过重新设计损失函数被无缝整合到训练过程中。重要的是，动态回归框架的参数与基础模型联合优化。我们在最先进的深度交通预测模型上，使用速度和流量数据集评估了所提框架的有效性，结果表明其性能得到提升，并提供了可解释的自回归系数和时空协方差矩阵。