Unlocking Multifractal and Long-Memory Dynamics in Cryptocurrency Markets: A Fractional Attention-Driven LSTM–N-BEATS Framework for Optimal Investment Under Dynamic Risk

Cryptocurrency markets exhibit persistent temporal dependence and multifractal scaling behavior, yet these properties remain only partially incorporated into existing deep learning architectures. This study proposes the Fractional Attention-Driven LSTM–N-BEATS (FA-LSTM-NBEATS) framework, integrating Grünwald–Letnikov fractional memory operators, adaptive attention, interpretable N-BEATS decomposition, and an asymmetric loss function within a unified forecasting and risk estimation model. The framework is evaluated using daily BTC, ETH, and BNB data from 2018 to 2025 through hierarchical ablation analysis, walk-forward validation, Diebold–Mariano testing, residual diagnostics, and Fractional Value-at-Risk (VaR) evaluation. Results indicate persistent scaling behavior with Hurst exponents above 0.76 and multifractal spectrum widths of Δα≈0.51–0.54. FA-LSTM-NBEATS acieves the strongest relative forecasting performance for BNB, with the lowest RMSE (0.02789) and MAE (0.01950) among all evaluated models. The learned fractional parameter α0.6106 remains stable across assets, suggesting convergence toward a persistent memory regime. In addition, Fractional VaR produces coverage ratios closer to unity than Historical and LSTM-based benchmarks under high-volatility conditions.