## Abstract

In this paper, the authors investigate the statistical properties of some cryptocurrencies by using three layers of analysis: alpha-stable distributions, Metcalfe’s law and the bubble behaviour through the LPPL modelling. The results show, in the medium to long-run, the validity of Metcalfe's law (the value of a network is proportional to the square of the number of connected users of the system) for the evaluation of cryptocurrencies; however, in the short-run, the validity of Metcalfe’s law for Bitcoin is questionable. As the results showed a potential for herding behaviour, the authors then used LPPL models to capture the behaviour of cryptocurrencies exchange rates during an endogenous bubble and to predict the most probable time of the regime switching. The main conclusion is that Metcalfe’s law may be valid in the long-run, however in the short-run, on various data regimes, its validity is highly debatable.

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