Probabilistic Forecasting Cryptocurrencies Volatility: From Point to Quantile Forecasts

ArXiv ID: 2508.15922 “View on arXiv”

Authors: Grzegorz Dudek, Witold Orzeszko, Piotr Fiszeder

Abstract

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. To 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 cryptocurrency realized variance. To 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.

Keywords: Probabilistic Forecasting, Quantile Estimation, Realized Volatility, Cryptocurrency Markets, Time Series Ensemble, Cryptocurrencies

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced statistical and machine learning methods, including quantile regression forests and multi-model stacking frameworks, requiring dense mathematical formulation. It demonstrates high empirical rigor with detailed data processing (log-transformed realized variance), a comprehensive backtest using Bitcoin data from 2017-2021, and robust evaluation metrics (CRPS, Winkler Score).

  flowchart TD
    A["Research Goal<br/>Forecast Cryptocurrency Volatility<br/>Using Probabilistic Methods"] --> B["Data Input<br/>Bitcoin Realized Variance<br/>(Log-Transformed)"]

    B --> C{"Methodology"}
    
    C --> D["Base Model Processing<br/>Statistical: HAR, GARCH, ARFIMA<br/>ML: LASSO, SVR, MLP, RF, LSTM"]
    
    D --> E["Probabilistic Framework<br/>Quantile Estimation via Residual Simulation<br/>- Linear Models<br/>- Stacking Ensemble"]
    
    E --> F["Computational Process<br/>Simulate Residuals<br/>Generate Quantile Predictions<br/>Estimate Conditional Distribution"]
    
    F --> G["Key Findings & Outcomes"]
    
    G --> H["QRS Method with Linear Base Models<br/>Optimal for Log-Volatility Data"]
    G --> I["Robust Probabilistic Stacking<br/>Comprehensive Risk Assessment"]
    G --> J["Significant Literature Gap Filled<br/>Practical Methodology for Crypto Markets"]