5G NR user equipment suffers from high power consumption due to continuous PDCCH monitoring. Predictive dynamic power management (DPM) can save energy by forecasting data grants, but accurate prediction is challenging due to unobservable scheduling states and bursty grant patterns. This paper proposes IOHMM-BO, a high-order input-output hidden Markov model with Bayesian optimization. Based on real 5G NR traces, we capture long-range dependencies via a compound state and jointly optimize model order and listening window using Bayesian optimization. Experiments on real traces show that IOHMM-BO achieves 45.3% accuracy, 5.0% false negative rate, and 43% energy saving with low computational overhead. The method provides a balanced trade-off between reliability and energy efficiency.

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