Modelling the vola tility of Ethereum returns using GARCH (1,1) under normal, student-t, and GED distributions

Abstract

This study investigates the volatility behaviour of Ethereum (Coinbase) returns using the Generalized Autoregressive Heteroskedasticity GARCH (1,1) model under three distributional assumptions: Normal, Student-t, and the Generalized Error Distribution (GED). Cryptocurrency markets are characterized by extreme price swings, heavy-tailed behaviour, and persistent volatility, making traditional constant-variance models ineffective. Descriptive statistics reveal strong deviations from normality in Ethereum returns, with high kurtosis (7.8454) and an extremely large Jarque–Bera statistic (1797.182 with its p-value less than 5%), indicating excess tail risk and frequent extreme movements. Preliminary analysis reveal that the return series is stationary, free from serial correlation, but exhibits significant ARCH effects, justifying the use of conditional heteroskedasticity models. Empirical results show highly persistent volatility across all models, with α + β values close to unity: approximately 0.99 under the Normal distribution, 1.01 under the Student-t specification, and 0.994 under GED distribution. Model comparison reveals that heavy-tailed error structures outperform the Normal model, with GED achieving the lowest AIC (−3.781), SIC (−3.7629), HQC (−3.7743), and the lowest MAPE (114.6606). These findings demonstrate that flexible distributional assumptions greatly enhance the modelling of extreme and persistent volatility in Ethereum returns. The study emphasizes the importance of adopting heavy-tailed GARCH frameworks when analysing cryptocurrency risk and forecasting volatility.