The Mathematics behind Cryptocurrencies "A Statistical Analysis of Cryptocurrencies"

Abstract

This article provides a statistical approach to describe the fit of the most popular cryptocurrencies, building off a previous report, "A Statistical Analysis of Cryptocurrencies." We examined Bitcoin, Ethereum, Tether, Binance, Ripple, Cardano, Solana, and Doge coins. To model our cryptocurrencies, we utilized trading prices between 2017 and 2022 in light of historic events, such as the COVID-19 pandemic. Additionally, we performed a correlation analysis to help understand the relationship between the popular cryptos. Here, we report that the candidate distributions we fit to model the currencies needed to be more independent to describe the return of all popular cryptos. This could be due to the need for Correlation between some of these popular cryptos. We found the generalized hyperbolic and the generalized t showed the best performance of the models tested, though these approaches remained limited in their overall fitness. Their performance also varied by cryptocurrency under investigation, with Tether demonstrating the worst fit across all candidate models. Using our fit models, we also predicted the average daily returns for January 1st, 2023, to February 1st, 2023, and generally found good predictive validity. These results are critical in understanding the movements of cryptos and help better understand the risk associated with trading these currencies.