In this paper, we propose an adaptive hybrid dynamic power management (AH-DPM) strategy based on a predictive shutdown scheme and an adaptive non-stationary stochastic process. The power consumption of AH-DPM, compared with the oracle algorithm (theoretical lower bound), is only 9.19% higher. Compare with other classical DPM algorithms, the power consumption of AH-DPM is 45.48% less than the static timeout algorithm, 17.45% less than an adaptive time out algorithm (Douglis et. al. [3]), and 20.93% less than a predictive shutdown algorithm (Huang et al. [7]). The uniqueness of the proposed AH-DPM is that it is designed for electronic components with multiple active/inactive states, and is thus applicable to handheld devices with ARM-based CPUs or IEEE 802.11 chipsets.