Volatility Analysis of Cryptocurrency Markets: A Comparative Study of EGARCH, LSTM and Hybrid Forecasting Models for Bitcoin and Ethereum
TL;DR
The principal finding is that the relative ranking of cryptocurrency volatility forecasts is highly sensitive to the choice of loss function but stable across alternative volatility proxies, indicating that the apparent superiority of LSTM models in cryptocurrency volatility forecasting is partly an artefact of evaluation under squared error.
Abstract
This paper compares econometric and deep learning approaches to one-day-ahead volatility forecasting for Bitcoin (BTC/USD) and Ethereum (ETH/USD) over the period from January 2016 to December 2025. Seven models are evaluated: a symmetric GARCH(1,1) with Student-t innovations, an asymmetric EGARCH(1,1) with Student-t innovations, a Long Short-Term Memory neural network, two hybrid LSTM specifications, a constant unconditional-variance benchmark, and a naive random walk. Hybrid-A augments the LSTM input with the EGARCH conditional variance forecast. Hybrid-B applies the LSTM to the standardised residuals of the fitted EGARCH model. To guard against the welldocumented sensitivity of recurrent neural networks to random initialisation, the LSTM-based models are estimated under ten different random seeds and the median forecast is reported. Squared daily log returns serve as the primary volatility proxy, with the Parkinson and Garman-Klass range-based estimators used as robustness benchmarks. Forecasts are produced through an expanding-window rolling scheme with monthly refits over the test period from January 2023 to December 2025, yielding 1,096 out-of-sample forecasts per model and asset. Statistical inference is based on the DieboldMariano test with the Harvey-Leybourne-Newbold correction and the Model Confidence Set procedure of Hansen, Lunde, and Nason (2011). The principal finding is that the relative ranking of cryptocurrency volatility forecasts is highly sensitive to the choice of loss function but stable across alternative volatility proxies. Under MSE, the LSTM achieves the lowest error and is the only model retained in the 90% Model Confidence Set for Ethereum, while several models survive jointly for Bitcoin. Under QLIKE, which is robust to noise in the squared-return proxy and penalises variance underestimation, both GARCH and EGARCH survive the Model Confidence Set jointly with the LSTM and Hybrid-B for Ethereum, and GARCH retains a place for Bitcoin. The LSTM-based models beat the constant unconditional-variance benchmark by 37% to 72% across proxies, confirming that the LSTM captures genuine volatility dynamics rather than merely predicting the mean. The variance-as-feature hybrid is dominated by the pure LSTM and exhibits substantially higher seed-to-seed variability than the other deep learning specifications, while the residual-based hybrid effectively collapses to the pure LSTM. Subperiod analysis confirms that these patterns are stable across the 2023, 2024, and post-spot-ETF 2025 windows. The findings indicate that the apparent superiority of LSTM models in cryptocurrency volatility forecasting is partly an artefact of evaluation under squared error and that simple parametric models retain a useful role under loss-consistent inference.