With Bitcoin, Ether and more than 2000 cryptocurrencies already forming a multi-billion dollar market, a proper understanding of their statistical and financial properties still remains elusive. Traditional economic theories do not explain their characteristics and standard financial models fail to capture their statistic and econometric attributes such as their extreme variability and heteroskedasticity. Motivated by these findings, we study Bitcoin and Ether prices via a Non-Homogeneous Pólya Gamma Hidden Markov (NHPG) model that has been shown to outperform its counterparts in conventional financial data. The NHPG algorithm has good in-sample performance and identifies both linear and non-linear effects of the predictors. Our results indicate that all price series are heteroskedastic with frequent changes between the two states of the underlying Markov process. In a somewhat unexpected result, the Bitcoin and Ether prices, although correlated, are significantly affected by different variables. We compare long term to short term Bitcoin data and find that significant covariates may change over time. Limitations of the current approach—as expressed by the large number of significant predictors and the poor out-of-sample predictions—back earlier findings that cryptocurrencies are unlike any other financial asset and hence, that their understanding requires novel tools and ideas.
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