Reliable ocean wave forecasts are critical for reducing the risk posed by extreme waves for ships and offshore infrastructure. Despite insights gained from theoretical investigations and constantly improving operational wave forecasting systems, the emergence of extreme waves remain unpredictable. In this article, the authors propose a data-driven modelling approach to generate high resolution wave forecasts for capturing individual waves, including rogue waves. To this end, a decomposition of the sea surface into a set of rapid oscillations and slowly varying amplitudes is utilized. The slow amplitude variations are subsequently forecasted by using universal, data-driven methods. In this approach, the extrapolation range of the data-driven techniques is extended by the slowness of the amplitude variations. The method's capabilities are demonstrated by using available measurements from an experimental wave tank and field data from ocean buoys.