Video stabilization is fundamental for providing good Quality of Experience for viewers and generating suitable content for video applications. In this scenario, Digital Video Stabilization (DVS) is convenient and economical for casual or amateur recording because it neither requires specific equipment nor demands knowledge of the device used for recording. Although DVS has been a research topic for decades, with a number of proposals from industry and academia, traditional methods tend to fail in a number of scenarios, e.g. with occlusion, textureless areas, parallax, dark areas, amongst others. On the other hand, defining a smooth camera path is a hard task in Deep Learning scenarios. This paper proposes a video stabilization system based on traditional and Deep Learning methods. First, we leverage Spatial Transformer Networks (STNs) to learn transformation parameters between image pairs, then utilize this knowledge to stabilize videos: we obtain the motion parameters between frame pairs and then smooth the camera path using moving averages. Our approach aims at combining the strengths of both Deep Learning and traditional methods: the ability of STNs to estimate motion parameters between two frames and the effectiveness of moving averages to smooth camera paths. Experimental results show that our system outperforms state-of-the-art proposals and a commercial solution.