The energy consumption of mobile networks is already substantial nowadays, and only expected to further increase with the roll-out of 5G. Base stations are the key elements in this context: reducing their energy consumption is of paramount importance for network operators, not only to lower operating costs, but also to meet sustainable development goals. Today's base stations are typically over-provisioned, i.e., they comprise multiple cells to meet the peak load in a region. Therefore, substantial energy savings are possible by switching off cells that are under-utilized. This article proposes a data-driven approach to determine the time periods when a cell can be switched off. Forecasting is used to accurately predict network utilization and automatically find the time intervals to reliably switch off a cell. We carefully analyze the requirements of the system as a whole, from data collection to forecasting methods, to enable effective energy savings in practice. Considering several real-world traces from LTE networks, we show that an average of 10.24% energy savings is possible. We explore the trade-offs between energy savings and overhead in switching off cells, and provide insights into the choice of methods accordingly. In particular, we show that the accuracy of forecasting is not the most important factor in achieving energy savings; instead, the prediction (uncertainty) interval plays a key role in being able to achieve energy savings with less impact on end-users. Finally, we propose a model to generate utilization traces that match the distribution of real-world traces obtained from cellular networks.