Fuzzy-Gated Stochastic Diffusion for Financial Regime Detection in Fractal Long-Memory Emerging Markets: The SARDINE Continuous-Time TSK Neuro-Fuzzy Framework

Financial markets in emerging economies exhibit fractal long-memory dynamics (H=0.93 on CBOE VIX; H=0.81 on JSE realised volatility) and extreme non-Gaussianity (kurtosis =51.6) that together invalidate conventional Gaussian-emission regime models. This paper introduces SARDINE (Stochastic Adaptive Regime Detection via Integrated Neuro-Fuzzy Estimation), a continuous-time framework that embeds Takagi-Sugeno-Kang (TSK) fuzzy membership weights directly inside a stochastic differential equation integrator, governing the geometry of stochastic uncertainty at each integration step. Three formal results underpin the architecture: a Lyapunov-style diffusion stability bound, a regime-adaptive noise attenuation guarantee, and an asymmetric cost advantage condition. Evaluated on 17 JSE Top40 securities (N=2778 daily observations, 2015–2026; 537-day held-out test), SARDINE achieves FAR =0.143, FNR =0.195, and a 1.33-day early-warning lead time, reducing the asymmetric cost by 32% relative to GMM. Against 14 baselines including Neural SDE, PatchTST, and Mamba, the fuzzy-gated diffusion reduces false alarms by 54–63%. A fractional Brownian motion ablation (H∈{0.44,0.50,0.93}, B=200 replicates) reveals that long-memory information should be embedded in the input representation rather than the noise driver; H=0.50 is recommended for operational deployment.