Long memory in the volatility of selected cryptocurrencies: Bitcoin, Ethereum and Ripple

This paper examines the volatility of cryptocurrencies, with particular attention to their potential long memory properties. Using daily data for the three major cryptocurrencies, namely Ripple, Ethereum, and Bitcoin, we test for the long memory property using, Rescaled Range Statistics (R/S), Gaussian Semi Parametric (GSP) and the Geweke and Porter-Hudak (GPH) Model Method. Our findings show that squared returns of three cryptocurrencies have a significant long memory, supporting the use of fractional Generalized Auto Regressive Conditional Heteroscedasticity (GARCH) extensions as suitable modelling technique. Our findings indicate that the Hyperbolic GARCH (HYGARCH) model appears to be the best fitted model for Bitcoin. On the other hand, the Fractional Integrated GARCH (FIGARCH) model with skewed student distribution produces better estimations for Ethereum. Finally, FIGARCH model with student distribution appears to give a good fit for Ripple return. Based on Kupieck's tests for Value at Risk (VaR) back-testing and expected shortfalls we can conclude that our models perform correctly in most of the cases for both the negative and positive returns.