Cyber attacks are a significant risk for cloud service providers and to mitigate this risk, near real-time anomaly detection and mitigation plays a critical role. To this end, we introduce a statistical anomaly detection system that includes several auto-regressive models tuned to detect complex patterns (e.g. seasonal and multi-dimensional patterns) based on the gathered observations to deal with an evolving spectrum of attacks and a different behaviours of the monitored cloud. In addition, our system adapts the observation period and makes predictions based on a controlled set of observations, i.e. over several expanding time windows that capture some complex patterns, which span different time scales (e.g. long term versus short terms patterns). We evaluate the proposed solution using a public dataset and we show that our anomaly detection system increases the accuracy of the detection while reducing the overall resource usage.