ABSTRACT
This study investigates the role of the probability distribution in forecasting the volatility and value-at-risk (VaR) of cryptocurrency returns using generalized auto-regressive conditional heteroskedasticity (GARCH)-type models. We consider GARCH, EGARCH, GJR-GARCH, TGARCH and Realized GARCH models and show that the role of the probability distribution varies across different situations. A skewed and heavy-tailed distribution contributes to better performance in forecasting the VaR; however, it does not improve the accuracy of volatility forecasting. The results help us to better understand the role of the probability distribution in GARCH-type models.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Data availability statement
The original data can be downloaded from https://firstratedata.com/b/31/crypto-active.
Notes
1 We obtain intraday data from https://firstratedata.com/b/31/crypto-active and employ a 5-min sampling frequency to estimate the realized kernel. The Oxford MFE Toolbox for MATLAB is used for this estimation.
2 We fit an AR (1) model for the conditional mean.
3 We use variance as a measure of volatility.
4 The leverage functions are specified as and
.
5 We can evaluate VaR models using this loss function because VaR is elicitable.