Explain Gaussian-copula degradation under extreme forecast-error stress

Explain why a Gaussian-copula dependence model performs worse than assuming no dependence under extreme forecast-error magnitudes, despite matching the empirical copula’s correlation structure and performing similarly at realistic error magnitudes.

Background

The paper compares three scenario-generation ensembles with identical per-zone marginals: an empirical dependence model, an independently sampled model, and a Gaussian-copula model. At realistic forecast-error magnitudes, the Gaussian copula is statistically indistinguishable from the empirical dependence model and modestly outperforms the independent model. Under an 8× forecast-error stress test, however, the Gaussian copula performs worse than the independent model, while the empirical model performs best.

The authors suggest that the Gaussian copula’s zero tail dependence may cause miscalibration of simultaneous-shortfall scenarios when interconnectors bind, but explicitly state that this explanation has not been fully verified. A rigorous explanation or characterization of the mechanism remains unresolved.