Local Gaussian Correlation in the Tails: A Scarcity Diagnostic, an Optimal Local Bandwidth, and the Limits of Adaptivity

Battle Count: 76

The paper is highly relevant for tail risk management, financial contagion detection, and portfolio allocation under asymmetric dependence. The finding that tail LGC is bounded by data scarcity (not bandwidth placement) is a cautionary message for practitioners relying on tail correlation estimates. The volatility-filtered equity return application (SPY/TLT, SPY/EEM) directly addresses common trading pairs. However, the narrow regime of adaptivity benefit and the inability to improve accuracy in the deepest tails limit direct trading signal generation. More relevant for risk management and portfolio construction than for high-frequency trading strategies.

The core LGC estimator is available in the R package 'localgauss'. The adaptive bandwidth requires: (1) a global-bandwidth pilot fit, (2) finite-difference estimation of the bias functional beta(x) involving Laplacian and gradient of the correlation surface, (3) density estimation from pilot effective sample size, (4) budget-neutral normalization, and (5) curvature stabilization with flooring and capping. The GARCH pre-whitening step adds complexity. The theoretical derivation is sophisticated (Hjort-Jones local likelihood specialized to Gaussian family), but the plug-in implementation is moderate. The main challenge is the regime-dependent behavior requiring practitioners to assess dependence strength before choosing global vs. adaptive.

All code, simulation harnesses, and figure scripts are openly available on GitHub. Monte Carlo uses deterministic cross-process seeding ensuring every reported number is reproducible. Real-data application fetches public daily prices and caches volatility-filtered residuals. The paper provides detailed Monte Carlo design specifications (copulas, parameters, grid points, replications).