Bitcoin returns and risk: A general GARCH and GAS analysis

Abstract This paper performs a general GARCH and GAS analysis for modelling and forecasting bitcoin returns and risk. Since Bitcoin trading exhibits excess volatility compared with other securities, it is important to model its risk and returns. We consider heavy-tailed GARCH models as well as GAS models based on the score function of the predictive conditional density of the bitcoin returns. We compare out-of-sample 1%-Value-at-Risk (VaR) forecasts under 45 different specifications using three backtesting procedures. We find that GAS models with heavy-tailed distributions provide the best out-of-sample forecast and goodness-of-fit properties to bitcoin returns and risk modelling. Normally-distributed GARCH models are always outperformed by heavy-tailed GARCH or GAS models. Besides, heavy-tailed GAS models provide the best conditional and unconditional coverage for 1%-VaR forecasts, illustrating the importance of modelling excess kurtosis for bitcoin returns. Hence, our findings have important implications for risk managers and investors for using bitcoin in optimal hedging or investment strategies.