Because of the accessibility of big data collections from consumers, products, and stores, advanced sales forecasting capabilities have drawn great attention from many businesses, especially those in retail, because of the importance of forecasting in decision making. Improvement of forecasting accuracy, even by a small percentage, may have a substantial impact on companies’ production and financial planning, marketing strategies, inventory controls, and supply chain management. Specifically, our research goal is to forecast the sales of each product in each store in the near future. Motivated by tensor factorization methodologies for context-aware recommender systems, we propose a novel approach called the advanced temporal latent factor approach to sales forecasting, or ATLAS for short, which achieves accurate and individualized predictions for sales by building a single tensor factorization model across multiple stores and products. Our contribution is a combination of a tensor framework (to leverage information across stores and products), a new regularization function (to incorporate demand dynamics), and extrapolation of the tensor into future time periods using state-of-the-art statistical (seasonal autoregressive integrated moving-average models) and machine-learning (recurrent neural networks) models. The advantages of ATLAS are demonstrated on eight product category data sets collected by Information Resources, Inc., where we analyze a total of 165 million weekly sales transactions of over 15,560 products from more than 1,500 grocery stores. Summary of Contribution: Sales forecasting has been a task of long-standing importance. Accurate sales forecasting provides critical managerial implications for companies’ decision making and operations. Improvement of forecasting accuracy may have a substantial impact on companies’ production planning, marketing strategies, inventory controls, and supply chain management, among other things. This paper proposes a novel computational (machine-learning-based) approach to sales forecasting and thus is positioned directly at the intersection of computing and business/operations research.