Large-scale and multidimensional spatiotemporal data sets are becoming ubiquitous in many real-world applications such as monitoring urban traffic and air quality. Making predictions on these time series has become a critical challenge due to not only the large-scale and high-dimensional nature but also the considerable amount of missing data... In this paper, we propose a Bayesian temporal factorization (BTF) framework for modeling multidimensional time series---in particular spatiotemporal data---in the presence of missing values. By integrating low-rank matrix/tensor factorization and vector autoregressive (VAR) process into a single probabilistic graphical model, this framework can characterize both global and local consistencies in large-scale time series data. The graphical model allows us to effectively perform probabilistic predictions and produce uncertainty estimates without imputing those missing values. We develop efficient Gibbs sampling algorithms for model inference and test the proposed BTF framework on several real-world spatiotemporal data sets for both missing data imputation and short-term/long-term rolling prediction tasks. The numerical experiments demonstrate the superiority of the proposed BTF approaches over many state-of-the-art techniques. (read more)