Quantile graphical models: Prediction and conditional independence with applications to systemic risk

Abstract

We propose two types of Quantile Graphical Models: (i) Conditional Independence Quantile Graphical Models (CIQGMs) characterize the conditional independence by evaluating the distributional dependence structure at each quantile index, as such, those can be used for validation of the graph structure in the causal graphical models; (ii) Prediction Quantile Graphical Models (PQGMs) characterize the statistical dependencies through the graphs of the best linear predictors under asymmetric loss functions. PQGMs make weaker assumptions than CIQGMs as they allow for misspecification. One advantage of these models is that we can apply them to large collections of variables driven by non-Gaussian and non-separable shocks. Because of QGMs’ ability to handle large collections of variables and focus on specific parts of the distributions, we could apply them to quantify tail interdependence. The resulting tail risk network can be used for measuring systemic risk contributions that help make inroads in understanding international financial contagion and dependence structures of returns under downside market movements.