Learning Adaptive Multi-Scale Memory Kernels in Fractional Stochastic Volterra Models: An AI-Assisted Framework for Financial Volatility

Abstract

Volatility persistence is inherently multi-scale, yet most fractional financial models impose the form and strength of memory before observing the data. This paper develops an AI-assisted fractional stochastic Volterra framework in which an interpretable dictionary of power-law memory kernels is learned sparsely and, when supported by the data, adapted across latent volatility regimes. Daily NIFTY 50 open–high–low–close observations from 2021–2025 are used, with Garman–Klass variance as the primary range-based volatility proxy. Candidate memory exponents β ∈ {0.1, . . . , 0.9} generate causal fractional-memory features, while a positive Elastic Net selects the active scales.  A three-state Gaussian

mixture model provides probabilistic calm, normal and stress regimes, and regime-specific fractional experts are combined by soft posterior gating. The framework is supplemented by a paper-specific product-integration consistency and convergence analysis, together with manufactured-solution verification. In the 2024 NIFTY 50 internal holdout, regime adaptation is detrimental at the 5-day horizon but materially improves the 20-day specification, reducing QLIKE from approximately 0.3650 for the static AI kernel to 0.2795. Against GARCH, GJR-GARCH, EGARCH, FIGARCH, HAR, EWMA and historical-volatility benchmarks, the 20-day fractional model attains the second-lowest volatility RMSE, although HAR remains superior under QLIKE. A supplementary zero-shot NIFTY-to-SPY transfer in 2026 yields the lowest RMSE and MAE among the tested SPY models, and the resulting risk scale produces well-calibrated 95% and 99% VaR backtests. The evidence therefore supports a horizon-dependent and regime-dependent interpretation of financial memory rather than universal forecasting dominance.