Unconditional and conditional heavy-tailed distributions for the returns of cryptocurrencies with a novel range exponential GARCH model

Abstract

This paper investigates which distribution is most appropriate for modeling the daily and hourly returns of cryptocurrencies. We study the distribution of both unconditional returns and conditional returns (innovations/residuals from a time-varying volatility model). We consider four well-known heavy-tailed distributions (Generalized Normal, Student t-, Normal Inverse Gaussian, Alpha stable) and two recently suggested distributions, and four GARCH models (plain GARCH, range GARCH, TGARCH and EGARCH). Moreover, we introduce a new GARCH model specification - a range exponential GARCH model, which combines the advantages of the RGARCH and EGARCH models. The results estimated for five cryptocurrencies (Bitcoin, Binance Coin, Ethereum, Solana, and Ripple) are unambiguous. For each cryptocurrency, the most appropriate distribution among the seven distributions included in this study is the generalized normal distribution. This conclusion holds not only for returns, but also for conditional returns (residuals from a conditional mean model in the presence of heteroscedasticity), and for all the considered volatility models. The newly introduced RE-GARCH model is superior to all other GARCH specifications for both daily and intraday hourly returns of cryptocurrencies.