Beyond GARCH: Kernel-Based Volatility and Tail-Risk Forecasting for Ethereum

Abstract

This paper studies volatility prediction for Ethereum in the post-Merge era. Using daily ETH/USD returns from 15 September 2022 to 23 April 2026, we compare standard GARCH(1,1), Heston-Nandi GARCH(1,1), cross-validated and aggregated EWMA predictors, and Nadaraya-Watson kernelregression predictors. The kernel forecasts are constructed from a rank-transformed state vector that captures recent volatility and signed-return conditions, allowing the conditional variance function to be nonlinear and state dependent. The results show that forecast performance is strongly horizon dependent. At the one-day horizon, the kernel predictor using the fitted GARCH volatility state delivers the lowest final cumulative squared prediction error, outperforming the standard GARCH benchmark and all EWMA-type competitors. At the ten-day-ahead horizon, the advantage of local nonparametric information weakens, and the mean-reverting structure of GARCH becomes more valuable. The estimated kernel surface reveals that predicted ETH volatility is highest when elevated recent volatility coincides with negative signed-return pressure. Conditional quantile results further show that kernel-based VaR improves lower-tail risk forecasts, especially at the 1% quantile. Overall, the evidence suggests that post-Merge Ethereum volatility is persistent, asymmetric, heavytailed, and nonlinear, and is best modelled by combining economically meaningful volatility states with flexible nonparametric forecasting maps.