In order to improve the energy efficiency and resource management of cellular networks, traffic modeling and prediction has been focused in recent years. In this paper, we take advantage of entropy theory to explore the limits of predictability of cellular network traffic based on large amount of traffic dataset gathered from real cellular network in China. By categorizing traffic according to voice, text and data group, we investigate random entropy of each type of traffic, as well as conditional entropy by temporal, spatial and service related information. Our key findings are that (1) traffic can be well predicted by preceding 15 hours traffic, (2) voice traffic has so close similarity to text traffic in the same cell that we can use one of them to predict the other, (3) knowledge of adjacent cells traffic can enhance the predictability of voice and text more than data. Considering the large amount traffic dataset which contains thousands of base stations and billions of records, the impact of dataset pre-processing, quantization and time resolution are also taken into account and are discussed. Moreover, macroscopic view of entropy distribution is presented by geo-location markers.