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Existing power management techniques operate by reducing performance capacity (frequency, voltage, size) when performance demand is low. In the case of multicore systems, the performance and power demand is the aggregate demand of all cores in the system. Monitoring aggregate demand makes detection of phase changes difficult since aggregate phase behavior obscures the underlying phases generated by the workloads on individual cores. This causes suboptimal power management and over-provisioning of power resources. In this paper, we address these problems through core-level, activity prediction. The core-level view makes detection of phase changes more accurate, yielding more opportunities for efficient power management. Due to the difficulty in anticipating activity level changes, existing operating system power management strategies rely on reaction rather than prediction. This causes sub-optimal power and performance since changes in performance capacity by the power manager lag changes in performance demand. To address this problem we propose the periodic power phase predictor (PPPP). This activity level predictor decreases SYSMark 2007 processor power consumption by 5.4% and increases performance by 3.8% compared to the reactive scheme used in Windows Vista operating system. Applying the predictor to the prediction of processor power, we improve accuracy by 4.8% compared to a reactive scheme.