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Extreme events have an important role which is sometime catastrophic in avariety of natural phenomena including climate, earthquakes and turbulence, aswell as in man-made environments like financial markets. Statistical analysisand predictions in such systems are complicated by the fact that on the onehand extreme events may appear as "outliers" whose statistical properties donot seem to conform with the bulk of the data, and on the other hands theydominate the (fat) tails of probability distributions and the scaling of highmoments, leading to "abnormal" or "multi"-scaling. We employ a shell model ofturbulence to show that it is very useful to examine in detail the dynamics ofonset and demise of extreme events. Doing so may reveal dynamical scalingproperties of the extreme events that are characteristic to them, and notshared by the bulk of the fluctuations. As the extreme events dominate thetails of the distribution functions, knowledge of their dynamical scalingproperties can be turned into a prediction of the functional form of the tails.We show that from the analysis of relatively short time horizons (in which theextreme events appear as outliers) we can predict the tails of the probabilitydistribution functions, in agreement with data collected in very much longertime horizons. The conclusion is that events that may appear unpredictable onrelatively short time horizons are actually a consistent part of a multiscalingstatistics on longer time horizons.Comment: 11 pages, 14 figures included, PRE submitte

Outliers, extreme events, and multiscaling