Probabilistic Forecasting of Long-Term Origin-Destination Demands: An Interpretable Bayesian Framework for Periodicity and Residual Learning

Origin-Destination (OD) demands are the backbone of traffic management and urban planning, serving as the fundamental input to numerous mobility applications. Existing studies mainly focus on modeling and predicting OD demands in the short term, while studies for long-term OD demand forecasting are limited. In particular, long-term OD demand prediction provides insights into the evolving spatiotemporal distribution of travel demands over extended periods, informing service scheduling and resource allocation that short-term forecasting cannot adequately support. One of the most distinguishing characteristics of OD demand time series is their inherent periodicity, punctuated by intermittent fluctuations. In view of this, we propose a novel interpretable Bayesian framework for long-term OD demand forecasting, which integrates both periodic patterns and transient fluctuations into a unified predictive model. By leveraging stochastic variational inference (SVI) and a modified tensor decomposition approach, the posterior distributions of the periodic and residual components in OD demands are formally derived. This enables the generation of both point-valued predictions and corresponding prediction intervals, which effectively quantify the predictive uncertainty and enhance model reliability. To validate the effectiveness of our proposed framework, we conduct experiments on real-world OD datasets. The results show that our model consistently outperforms state-of-the-art deep learning approaches under diverse scenarios. This underscores the effectiveness and robustness of our model in addressing the challenges of long-term multiple OD demand forecasting.