HK-DeepIV: heat-kernel geometric diagnostics and early-warning signals for curvature-induced interference in financial correlation networks

Résumé

Financial correlation networks under infrastructure shocks undergo curvature-driven interference that standard estimators cannot detect. This study introduces Heat-Kernel Deep Instrumental Variables (HK-DeepIV), a geometric diagnostic and early-warning framework modeling shock propagation as heat diffusion on the Riemannian manifold of Johannesburg Stock Exchange (JSE) asset-return correlations. Three formal results underpin the architecture: a non-parametric identification result for the projection of the structural function onto the leading heat-kernel eigenfunction ( k = 1; a scalar instrument can identify at most one linear combination of the eigenfunctions, and no claim is made beyond that projection); double robustness via Neyman orthogonality; and Corollary 3.2, showing that unit-level distinguishability collapses exponentially in diffusion time whenever Ollivier-Ricci curvature is positive; a purely geometric statement providing the basis for the fragility diagnostics developed here. Applied to 60 JSE tickers (2,832 trading days, 2015–2025) with Eskom load-shedding as the treatment (2022–2025), the trained model produces an ATE of +383 bp, reported as an overfitting artifact. Five independent baselines converge on smaller, mostly negative estimates. The most credibly conditioned conditional-association estimate is double machine learning [−20.75 bp, heteroskedasticity-and-autocorrelation-consistent (HAC)-corrected 95% CI [−51.62, 10.12] bp, p = 0.188], which is not significant at conventional levels; consistent with the instrument exogeneity caveat (5-day lagged return balance test, p = 0.007) and the descriptive framing of all estimates. The instrument [48-h-ahead Eskom stage forecast, Corr( Z t , D t )≈0.71, first-stage F = 47.3] is distinct from the treatment (realized Stage ≥2 binary), but exogeneity is not confirmed; all estimates are conditional associations. The Fiedler eigenvalue (mean 0.3827, minimum 0.1819) and mean Ollivier-Ricci curvature (0.5517, persistently positive) provide computable real-time fragility indicators. Across the four most severe load-shedding quarters, Fiedler and Ricci diagnostics offer comparable early-warning signals (mean lead-time difference −0.5 trading days); neither is systematically superior, but their combination is more informative than either alone. The framework contributes toward real-time spectral monitoring of infrastructure-driven systemic risk, supporting Uited Nations Sustainable Development Goal (UN SDG 9) in emerging markets.

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