The knowledge of the upper bounds of mobile data traffic predictors provides not only valuable insights on human behavior but also new opportunities to reshape mobile network management and services as well as provides researchers with insights into the design of effective prediction algorithms. In this paper, we leverage two large-scale real-world datasets collected by a major mobile carrier in a Latin American country to investigate the limits of predictability of cellular data traffic demands generated by individual users. Using information theory tools, we measure the maximum predictability that any algorithm has potential to achieve. We first focus on the predictability of mobile traffic consumption patterns in isolation. Our results show that it is theoretically possible to anticipate the individual demand with a typical accuracy of 85% and reveal that this percentage is consistent across all user types. Despite the heterogeneity of users, we also find no significant variability in predictability when considering demographic factors or different mobility or mobile service usage. Then, we analyze the joint predictability of the traffic demands and mobility patterns. We find that the two dimensions are correlated, which improves the predictability upper bound to 90% on average.