The potential to create extreme events is an inherent property of complex systems. Since our highly structured society is particularly sensitive to extreme events such as larger power failures in electric networks, stock market crashes, epedemics caused by new types of viruses, flash floods by summer storms, their potential predictability is of highest relevance. In this contribution we assume a physical point of view and concentrate on a specific phenomenon, namely on turbulent wind gusts. We show how a rather general model, namely a continuous state Markov chain, can be employed for data driven predictions of strong wind gusts. A Markov chain can represent arbitrary finite memory processes within the range of deterministic chaotic systems on the one extreme to uncorrelated white noise on the other, but its particular strenght lies in between: Nonlinear stochastic processes. Clearly, the modelling of the turbulent flow at a single site by a Markov chain is an approximation, whose accuracy will be discussed in the talk. From a statistical point of view, the focus on the prediction of extreme events implies the usage of unconventional cost junctions, such that our predictor does not neccessarily perform well on "normal" bulk events, but has a surprisingly good performance on extreme events.