Diagnosing and Stabilizing Dynamic Correlations in Multivariate Stochastic Volatility Models

Adding flexibility to a multivariate volatility model can worsen covariance forecasts; we show when, and how to detect it. We decompose the multivariate QLIKE loss into trace, marginal-scale, and correlation log-determinant components; counterfactual block substitutions attribute gains or losses to either part. In Bayesian dynamic-correlation stochastic volatility, the diagnostic yields a sequence: diffuse dynamic correlations can underperform a constant-correlation baseline; a stabilizing prior repairs the correlation component; once stabilized, lagged realized-volatility inputs are the strongest remaining lever, with neural corrections competitive but not dominant. Under a rolling protocol, the stabilized realized-augmented family rivals realized-covariance benchmarks while retaining full predictive densities.