An Empirical Comparison of GARCH-Type Models for Cryptocurrency Volatility Forecasting

This study investigates the volatility dynamics of Bitcoin (BTC), Ethereum (ETH), and Binance Coin (BNB) from 1 January 2021 to 31 December 2025. Using daily return data, the study applies Generalized Autoregressive Conditional Heteroskedasticity (GARCH)(1,2), Exponential GARCH (EGARCH)(1,2), and Power ARCH (PARCH)(1,2) models to examine conditional volatility, persistence, and asymmetric responses to shocks. The three cryptocurrencies differ substantially in distributional characteristics: BNB exhibits the highest variability, positive skewness, and excess kurtosis, indicating more extreme returns. The Augmented Dickey–Fuller test confirms that all three series are stationary, while the ARCH Lagrange Multiplier (LM) test indicates significant ARCH effects, supporting GARCH-family models. The estimated models show that volatility depends on recent shocks and past conditional volatility, is highly persistent in all three markets, and differs across the cryptocurrencies. The estimated asymmetry coefficients differ in sign and size across assets, but their significance cannot be established from the reported estimates. Diagnostic tests indicate no significant residual autocorrelation or remaining ARCH effects at the 5% level. Forecast evaluation using Root Mean Square (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and the Theil coefficient over 10-, 30-, and 60-period horizons shows similar performance across models, varying by cryptocurrency, horizon, and measure, with no model consistently superior. Overall, the findings highlight the heterogeneity of cryptocurrency volatility and the importance of comparing alternative models.