Statistical Analysis of Returns from Cryptocurrencies at Varying Frequencies: Failure of Cubic Law

Statistical analysis of returns for four popular cryptocurrencies viz. Bitcoin, Ethereum, Ripple and Litecoin is carried out at varying frequencies. It is found that q-Gaussian distribution fits well to empirical distribution of normalized returns for all the four cryptocurrencies at daily, hourly and minute level. A new method based on Kolmogorov-Smirnov statistic is proposed to estimate the distribution parameter
$q$
. The analysis also reveals that normalized returns from cryptocurrencies depict power law with scaling parameter of 2.66, thus violating the cubic law of returns observed in traditional financial markets. The conformation of q-Gaussian distribution across various distinct cryptocurrencies indicate that underlying dynamics of them is identical and they belong to same universality class. These results will help in making better investment decisions and trading strategies.