A general hierarchical statistical framework for the characterization of wind turbulence is proposed. This framework should ease the understanding of different existing statistical approaches and enable a clear path for refined methods of characterization. Low-order statistical descriptions were extended by higher-order statistics with respect to one-point and two-point statistics. In particular, we showed that proper analysis leads to a superstatistics approach for the probability of velocity fluctuations. To demonstrate the importance of our considerations, we analysed wind time series of the research platform FINO 1. On one side, we showed how different statistical aspects can be reproduced quite accurately, whereas on the other, the necessity of more profound approaches was worked out. The analysis of the measured data provides some deep insights into the nature of wind turbulence. Most interestingly, for conditioned data subsets, we found higher-order statistical behavior well known for idealized turbulence. Finally, we give an outlook on how to achieve a general n-point statistical description. Copyright © 2011 John Wiley & Sons, Ltd.