Super-extreme events in the form of sustained drifts and abrupt shocks are analysed both numerically and analytically; in particular their impact on velocity autocorrelation function is discussed. Our theoretical model is based on the hierarchical Weierstrass-Mandelbrot Continuous-Time Random Walk formalism. We also discuss the possibility of an unambiguous distinction between the super-extreme ``dragon-kings'' and `normal' ``black swans'' in real empirical time series.

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