Probabilistic forecasting of high-frequency realized cryptocurrency volatility via CEEMDAN-integrated autoregressive recurrent neural network

This study introduces CEEMDAN–DeepAR, a deep learning framework for probabilistic forecasting of high-frequency realized volatility in cryptocurrency markets. The model integrates complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and an autoregressive recurrent neural network (DeepAR) to capture the complex, nonlinear, and volatile dynamics of cryptocurrency. Unlike conventional approaches limited to point forecasts, the proposed framework produces calibrated predictive distributions that quantify both central tendencies and tail risks, which are essential for risk management. A rolling-window CEEMDAN decomposition is employed to extract intrinsic mode functions as covariates, eliminating data leakage and enabling real-time applicability. Extensive experiments on six major cryptocurrencies across different market regimes demonstrate that CEEMDAN–DeepAR consistently outperforms statistical baselines and deep learning alternatives. Importantly, the integration of CEEMDAN enhances performance across all deep learning architectures, yielding more accurate point forecasts and tighter, better-calibrated prediction intervals. The model remains robust under volatility shifts and extreme market conditions, avoiding excessive widening of uncertainty bands. In addition, a utility-based economic value analysis confirms that forecast improvements translate into superior portfolio outcomes, showing the practical value of distributional forecasting. Overall, the results highlight CEEMDAN-based integration as a powerful enhancement to deep learning models, with CEEMDAN–DeepAR in particular emerging as a highly effective, scalable, and reliable solution for high-frequency volatility forecasting in cryptocurrency markets.