The Cloud-RAN (C-RAN) paradigm is envisioned to increase the efficiency of future mobile networks by moving the computational resources needed at the Remote Radio Heads (RRH) to the cloud infrastructure. In this work, we provide a framework that optimizes the number of allocated virtual resources by considering both the computational requirements of the RRH and the Quality of Service of users, which could experience loss of service due to reassociations between the RRH and the virtual machines. The provided optimization framework is supported by data coming from a real mobile network of a middle-sized European city, which provides an estimate for the computational loads coming from the RRH. We evaluate the performance of the framework in different scenarios, analyzing the impact of different forecasting algorithms as well as different look-ahead intervals for the predictions (short-term / long-term). The results obtained by our framework can be used to assist network operators in the optimization of C-RAN resources and shed some light on the interplay between forecasting errors and overall performance.