Chapter 10 Criticality of the Bitcoin Market

Abstract

Perhaps the most intriguing characteristics of Complex Systems arise while they undergo phase transition phenomena. Indeed, some of the real world’s most complex systems enter critical regimes, either as a result of (not necessarily identifiable) slowly varying parameters’ alteration, or spontaneously, due to self-tuning towards criticality. We discuss two toy models of such critical behaviour introducing the key principles particularly suited for their analysis and characterisation. This is followed by exploring one of such characteristics, namely the non-Gaussianity of event size distribution in a real-life complex system of the stock market. Two markets are investigated: Bitcoin and S&P by extracting variance λ2 with the help of Castaing’s equation from batches of different lengths from ∼month to ∼year. We first focus on the scale dependence of variance λ2, which is then enriched by the analysis of the dynamics of λ2 across subsequent batches We show, that the increase of λ2 occurs in all batch perspective and might serve as a warning signal for an incoming crash.