A Factor-Copula Latent-Vine Time Series Model for Extreme Flood Insurance Losses

Statistical inference on the dependence of multivariate extremes poses notable challenges, particularly in contexts characterized by large dimensions and sparse extreme observations. While copula models provide flexible parametric methods for dependence modeling, caution is warranted when using them for extremal dependence inference or tail extrapolation. In this article, a novel class of factor-vine copula models is introduced. It is designed for modeling the dependence of extreme insurance losses within the context of the National Flood Insurance Program (NFIP), with broader applicability to space-time dependence modeling in multivariate time series data featuring a clustering structure. The proposed model is a specialized graphical vine dependence model with a latent factor structure. It integrates the advantages of both vine and factor copulas by allowing for great flexibility in tail dependence modeling while maintaining interpretability through a parsimonious latent structure. It is also shown how the incorporation of univariate extreme-value margins and tail-weighted dependence measures within the factor-vine model can address current challenges associated with using parametric copulas for extreme inference. Applications of the proposed model are discussed in the context of the NFIP, focusing on its efficacy in evaluating the risks associated with extreme weather events. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.