Abstract-Traffic learning and prediction is at the heart of the evaluation of the performance of telecommunications networks and attracts a lot of attention in wired broadband networks. Now, benefiting from the big data in cellular networks, it becomes possible to make the analyses one step further into the application level. In this paper, we firstly collect a significant amount of application-level traffic data from cellular network operators. Afterwards, with the aid of the traffic "big data", we make a comprehensive study over the modeling and prediction framework of cellular network traffic. Our results solidly demonstrate that there universally exist some traffic statistical modeling characteristics at a service or application granularity, including α-stable modeled property in the temporal domain and the sparsity in the spatial domain. But, different service types of applications possess distinct parameter settings. Furthermore, we propose a new traffic prediction framework to encompass and explore these aforementioned characteristics and then develop a dictionary learning-based alternating direction method to solve it. Finally, we examine the effectiveness and robustness of the proposed framework for different types of application-level traffic. Our simulation results prove that the proposed framework could offer a unified solution for application-level traffic learning and prediction and significantly contribute to solve the modeling and forecasting issues.