Predicting the volatility of cryptocurrencies' returns using high-frequency data : a comparative analysis of GARCH, EGARCH, IGARCH, GJR-GARCH, LRE, and HAR models

This study provides a comprehensive evaluation of six volatility forecasting models applied to twelve dominant and less dominant cryptocurrencies across multiple time horizons using high-frequency intraday data. The exponential generalized autoregressive conditional heteroskedastic (EGARCH), integrated GARCH (IGARCH), standard GARCH, GJR-GARCH, lagged realized volatility (LRE), and heterogeneous autoregressive (HAR) models are systematically compared using 5 min computed return data from September 2018 to September 2020. Our analysis encompasses three forecast horizons (1-day, 7-day, and 30-day) to assess model performance under varying temporal constraints. Through univariate Mincer-Zarnowitz regressions, encompassing tests, and out-of-sample evaluation using root mean squared error (RMSE) and quasi-likelihood loss (QLIKE) functions, we identify significant performance heterogeneity across models and cryptocurrencies. The HAR model exhibits stronger predictive accuracy at short horizons, while EGARCH exhibits relatively stronger performance at longer horizons, although overall explanatory power declines as forecast horizon increases. Importantly, no single model consistently provides optimal forecasts across all cryptocurrencies. Consistent with prior evidence suggesting model performance varies across assets. Encompassing regressions reveal that combining HAR with EGARCH specifications significantly enhances explanatory power across all temporal frames. Out-of-sample Diebold-Mariano tests indicate that HAR generates the lowest forecast errors for most cryptocurrencies, though EGARCH performs exceptionally well for high-market-capitalization assets. These findings provide regime-conditional insights into horizon- and asset-specific volatility dynamics during the pre-institutionalization phase of cryptocurrency markets. The study contributes to emerging literature by incorporating less-dominant cryptocurrencies and offering robust empirical evidence on the asymmetric and persistent volatility characteristics unique to digital asset markets. These findings should be interpreted within the context of the 2018-2020 sample period, representing a pre-institutionalized phase of cryptocurrency markets, and may not fully generalize to structurally different market regimes characterized by increased institutional participation and regulatory development.