A cryptocurrency empirical study focused on evaluating their distribution functions

Abstract

This paper thoroughly examines the statistical properties of cryptocurrency returns, particularly focusing on studying which is the best statistical distribution for fitting this type of data. The preliminary statistical study reveals (i) high volatility, (ii) an inverse leverage effect, (iii) skewed distributions and (iv) high kurtosis. To capture the nonnormal characteristics observed in cryptocurrency data, we verified the goodness of fit of a large set of distributions, both symmetric and skewed distributions such as skewed Student-t, skewed generalized t, skewed generalized error and the inverse hyperbolic sign distributions. The results show that the skewed distributions outperform normal and Student-t distributions in fitting cryptocurrency data, although there is no one skewed distribution that systematically better fits the data. In addition, we compare these distributions in terms of their ability to forecast the market risk of cryptocurrencies. In line with the results obtained in the statistical analysis, we find that the skewed distributions provide better risk estimates than the normal and Student-t distributions, both in short and long positions, with SGED being the distribution that provides better results.