In this paper, we examine several aspects of volatility for the 50 largest cryptocurrencies. For instance, we study the standard deviation and variance of returns, the autocorrelation of absolute and squared returns, the beta of returns vis-à-vis Bitcoin, the leverage effect of cryptocurrency returns versus the standard deviation of returns and how calendar effects impact the magnitude of cryptocurrency price returns. As far as we know, this is the most exhaustive study done to date on cryptocurrency returns and volatility.

We conduct a systematic study on the statistical properties of returns of the two major cryptocurrencies, Bitcoin and Ether. We further estimate six popular GARCH models for the BTC and ETH return series and find that the two-component GJR model has the best fit overall.