Relevant stylized facts about bitcoin: Fluctuations, first return probability, and natural phenomena

Abstract

Bitcoin is a digital financial asset that is devoid of a central authority. This makes it distinct from traditional financial assets in a number of ways. For instance, the total number of tokens is limited and it has not explicit use value. Nonetheless, little is know whether it obeys the same stylized facts found in traditional financial assets. Here we test bitcoin for a set of these stylized facts and conclude that it behaves statistically as most of other assets. For instance, it exhibits aggregational Gaussianity and fluctuation scaling. Moreover, we show by an analogy with natural occurring quakes that bitcoin obeys both the Omori and Gutenberg-Richter laws. Finally, we show that the global persistence, originally defined for spin systems, presents a power law behavior with exponent similar to that found in stock markets.