Risk management via contemporaneous and temporal dependence structures with applications.

This paper presents the estimation methods of the Bayesian Graphical Vector Auto-regression with and without innovations such as external regressors (BG-VARX) and Bayesian Graphical Systems Equation Modelling (BG-SEM), which are developed to examine risk network structures embedded in multivariate time series. This methodical approach allows for the analysis of various dynamics and persistence in the multivariate time series in terms of risk propagation. For instance, both the BG-SEMX and BG-VARX can reveal the within-day and across-day major risk transmitters as well as risk recipients from other univariate time series, which better explain risk contagion using complex network models. In addition, the procedures for models with and without exogenous variables have been explored, which shows that the former produces more network structures compared to the latter and therefore depicts their influential role. This approach, therefore, provides a platform for future research in terms of extension of the method to encompass different types of multivariate data with additional innovations that might aid feasible analysis and the design of policy instruments, and the implementation of relevant policy implications.