Prof. Mingli Chen
(Department of Economics, University of Warwick)
Quantile Graphical Models: Prediction and Conditional Independence with Applications to Financial Risk Management.
We propose Quantile Graphical Models (QGMs) to characterize predictive and conditional independence relationships within a set of random variables of interest.
This framework is intended to quantify the dependence in non-Gaussian settings which are ubiquitous in many econometric applications.
We consider two distinct QGMs. First, Condition Independence QGMs characterize conditional independence at each quantile index revealing the distributional dependence structure.
Second, Predictive QGMs characterize the best linear predictor under asymmetric loss functions.
Under Gaussianity these notions essentially coincide but non-Gaussian settings lead us to different models as prediction and conditional independence are fundamentally different properties.
Combined the models complement the methods based on normal and nonparanormal distributions that study mean predictability
and use covariance and precision matrices for conditional independence.