Fitting Dynamic Conditional Densities to Cross-Sectional Returns with Persistent Tail Intensities

We propose dynamic conditional densities with spline mixtures (DCD-SM) to detect whether the tail intensity of financial returns depends on past information after accounting for volatility and tail-order dynamics. The target is a weighted mixture of the conditional return densities of individual assets in a cross section. Individual distributions may differ, and returns within a date may be dependent. A normalized spline-mixture correction uses score-driven updates to change left and right tail intensities while preserving the reference tail order. We use Wald tests for persistence and assess empirical size, power, and forecast stability in simulations. With fitted references that have dynamic tail order, Wald tests at the nominal five-percent level detect dynamics that affect both tail intensities in the same direction in all 19 US and Japanese equity cross sections, for both raw returns and residuals after principal-component removal with training-fixed loadings. Evidence for dynamics in the imbalance between the two tail intensities is more limited. In the residuals, the correction improves out-of-sample one-percent lower-tail quantile loss relative to these references in 16 of 19 panels, with three significant positive differences at the five-percent level. Forecast gains are most evident in log scores and one-percent quantile losses and are less uniform for five-percent quantile loss.