Probabilistic Forecasting Cryptocurrencies Volatility: From Point to Quantile Forecasts

--Cryptocurrency markets are characterized by extreme volatility, making accurate forecasts essential for effective risk management and informed trading strategies. Traditional deterministic (point) forecasting methods are inadequate for capturing the full spectrum of potential volatility outcomes, underscoring the importance of probabilistic approaches. T o address this limitation, this paper introduces probabilistic forecasting methods that leverage point forecasts from a wide range of base models, including statistical (HAR, GARCH, ARFIMA) and machine learning (e.g. LASSO, SVR, MLP, Random Forest, LSTM) algorithms, to estimate conditional quantiles of cryp-tocurrency realized variance. T o the best of our knowledge, this is the first study in the literature to propose and systematically evaluate probabilistic forecasts of variance in cryptocurrency markets based on predictions derived from multiple base models. Our empirical results for Bitcoin demonstrate that the Quantile Estimation through Residual Simulation (QRS) method, particularly when applied to linear base models operating on log-transformed realized volatility data, consistently outperforms more sophisticated alternatives. Additionally, we highlight the robustness of the probabilistic stacking framework, providing comprehensive insights into uncertainty and risk inherent in cryptocurrency volatility forecasting. This research fills a significant gap in the literature, contributing practical probabilistic forecasting methodologies tailored specifically to cryptocurrency markets. Probabilistic forecasting of cryptocurrency volatility is essential due to the considerable uncertainty and frequent occurrence of extreme price movements in cryptocurrency markets. Unlike traditional point forecasts, probabilistic methods estimate the entire conditional distribution (or its fine-grained approximation using densely spaced quantiles) of future volatility, thereby capturing the full range of potential outcomes and significantly improving risk assessment and decision-making in these highly unpredictable markets. Despite these clear benefits, probabilistic forecasting methods remain relatively scarce in the cryptocurrency volatility literature.