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

Despite the popularity of Bitcoin as a new kind of financial asset, little is know whether it obeys the same stylized facts found in traditional financial instruments. Here we test Bitcoin for a set of these stylized facts. First we study the tails of the distribution of returns for Bitcoin and show that they are fat and exhibit aggregational Gaussianity. We then show that the volatility of Bitcoin tends to cluster in time. Also, the correlation between the volume and volatility is always positive, and the long range variance of returns predict the fine structure better than the other way around. In the second part of this work we show per analogiam that Bitcoin mimics a set of naturally occurring phenomena. For instance, the volatility observed in Bitcoin follows 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 traditional financial markets.