Volatility Evaluation Using Conditional Heteroscedasticity Models on Bitcoin, Ethereum and Ripple

Abstract: This study examines and compares the volatility in sample fit and out of sample forecast of four different heteroscedasticity models, namely ARCH, GARCH, EGARCH and GJR-GARCH applied to Bitcoin, Ethereum and Ripple. The models are fitted over the period from 2016-01-01 to 2019-01-01 and then used to obtain one day rolling forecasts during the period from 2018-01-01 to 2019-01-01. The study investigates three different themes consisting of the modelling framework structure, complexity of models and the relation between a good in sample fit and good out of sample forecast. AIC and BIC are used to evaluate the in sample fit while MSE, MAE and R2LOG are used as loss functions when evaluating the out of sample forecast against the chosen Parkinson volatility proxy. The results show that a heavier tailed reference distribution than the normal distribution generally improves the in sample fit, while this generality is not found for the out of sample forecast. Furthermore, it is shown that GARCH type models clearly outperform ARCH models in both in sample fit and out of sample forecast. For Ethereum, it is shown that the best fitted models also result in the best out of sample forecast for all loss functions, while for Bitcoin non of the best fitted models result in the best out of sample forecast. Finally, for Ripple, no generality between in sample fit and out of sample forecast is found.