Private and public clouds require users to specify requests for resources such as CPU and memory (RAM) to be provisioned for their applications. The values of these requests do not necessarily relate to the application's run-time requirements, but only help the cloud infrastructure resource manager to map requested resources to physical resources. If an application exceeds these values, it might be throttled or even terminated. As a consequence, requested values are often overestimated, resulting in poor resource utilization in the cloud infrastructure. Autoscaling is a technique used to overcome these problems. We observed that Kubernetes Vertical Pod Autoscaler (VPA) might be using an autoscaling strategy that performs poorly on workloads that periodically change. Our experimental results show that compared to VPA, predictive methods based on Holt-Winters exponential smoothing (HW) and Long Short-Term Memory (LSTM) can decrease CPU slack by over 40% while avoiding CPU insufficiency for various CPU workloads. Furthermore, LSTM has been shown to generate stabler predictions compared to that of HW, which allowed for more robust scaling decisions.