Cloud computing depends on the dynamic allocation and release of resources, on demand, to meet heterogeneous computing needs. This is challenging for cloud data centers, which process huge amounts of data characterised by its high volume, velocity, variety and veracity (4Vs model). Managing such a workload is increasingly difficult using state-of-the-art methods for monitoring and adaptation, which typically react to service failures after the fact. To address this, we seek to develop proactive methods for predicting future resource exhaustion and cloud service failures. Our work uses a realistic test bed in the cloud, which is instrumented to monitor and analyze resource usage. In this paper, we employed the optimal Kalman filtering technique to build a predictive and analytic framework for cloud server KPIs, based on historical data. Our k-step-ahead predictions on historical data yielded a prediction accuracy of 95.59%. The information generated from the framework can best be used for optimal resources provisioning, admission control and cloud SLA management.