Bayesian Spike-and-Slab Finite Mixture with Adaptive Tail Regularisation for Robust Volatility Regime Identification: Evidence from the Johannesburg Stock Exchange

Volatility regime identification underpins risk management and portfolio allocation in quantitative finance, yet standard mixture models fail in heavy-tailed environments: components are consumed by outliers rather than genuine persistent regimes. We propose the Bayesian Spike-and-Slab Finite Mixture with Adaptive Tail Regularisation (BSS-FM-ATR), which resolves this at the component level via a spike-and-slab prior on the degrees-of-freedom parameter νk. A latent binary indicator assigns each component to a slab state (data-driven tail adaptation for genuine regimes) or a spike state (inert heavy-tail absorber for artefacts). Applied to 19 JSE blue-chip securities over December 2019 to December 2025—spanning the COVID-19 crash and Eskom load-shedding episodes—BSS-FM-ATR achieves the highest silhouette score (0.3809 on the full dataset), regime persistence (0.9391), and interpretability (0.800) across nine standard baselines, including Gaussian HMM, MS-AR, MS-GARCH(1,1), and Bayesian Changepoint detection, plus three outlier-component comparators (Contaminated–Normal Mixture, TCLUST, and robust Bayesian mixture). A complete rerun after removing the contaminated observations confirms that ARI (Δ=−0.0283) and persistence (Δ=+0.0105) remain stable; the silhouette reduction (from 0.3809 to 0.3773) is a positive finding: it confirms that the spike-state component R3 was correctly identified as a compact, well-separated artefact cluster whose removal reveals the genuine regime structure. This dual validation establishes BSS-FM-ATR’s role as both a regime identifier and a data quality filter. The method isolates a Yahoo Finance data-contamination artefact (n=21, January–February 2025) through a principled spike-and-slab mechanism, providing an explicit posterior probability p(γ3=0∣X)>0.99 of artefact status: a structural identifier that contaminated-normal and robust Bayesian alternatives cannot supply, establishing its value as both a regime identifier and a data quality filter for financial monitoring systems.