Objective: Acute intracranial hypertension is an important risk factor of secondary brain damage after traumatic brain injury. Hypertensive episodes are often diagnosed reactively, leading to late detection and lost time for intervention planning. A pro-active approach that predicts critical events several hours ahead of time could assist in directing attention to patients at risk. Approach: We developed a prediction framework that forecasts onsets of acute intracranial hypertension in the next 8 h. It jointly uses cerebral auto-regulation indices, spectral energies and morphological pulse metrics to describe the neurological state of the patient. One-minute base windows were compressed by computing signal metrics, and then stored in a multi-scale history, from which physiological features were derived. Main results: Our model predicted events up to 8 h in advance with an alarm recall rate of 90% at a precision of 30% in the MIMIC-III waveform database, improving upon two baselines from the literature. We found that features derived from high-frequency waveforms substantially improved the prediction performance over simple statistical summaries of low-frequency time series, and each of the three feature classes contributed to the performance gain. The inclusion of long-term history up to 8 h was especially important. Significance: Our results highlight the importance of information contained in high-frequency waveforms in the neurological intensive care unit. They could motivate future studies on pre-hypertensive patterns and the design of new alarm algorithms for critical events in the injured brain.