Bayesian Graphical Models for STructural Vector Autoregressive Processes

Abstract

Vector autoregressive models have widely been applied in macroeconomics and macroeconometrics to estimate economic relationships and to empirically assess theoretical hypothesis. To achieve the latter, we propose a Bayesian inference approach to analyze the dynamic interactions among macroeconomics variables in a graphical vector autoregressive model. The method decomposes the structural model into multivariate autoregressive and contemporaneous networks that can be represented in the form of a directed acyclic graph. We then simulated the networks with an independent sampling scheme based on a single-move Markov Chain Monte Carlo (MCMC) approach. We evaluated the efficiency of our inference procedure with a synthetic data and an empirical assessment of the business cycles hypothesis.

Sparse Bayesian time-varying covariance estimation in many dimensions

“…For related work on sparse Bayesian prior distributions in high dimensions, see e.g. Kaufmann and Schumacher (2013) who use a point mass prior specification for factor loadings in dynamic factor models or Ahelegbey et al (2016) who use a graphical representation of vector autoregressive models to select sparse graphs. From a mathematical point of view, Pati et al (2014) investigate posterior contraction rates for a related class of continuous shrinkage priors for static factor models and show excellent performance in terms of posterior rates of convergence with respect to the minimax rate.…”

CoRisk: Credit Risk Contagion with Correlation Network Models

“…To address systemic risks, correlation network models that combine financial networks (see, e.g., Lorenz et al (2009) and Battiston et al (2012)) with contagion models based on the dependence structure among market prices have been proposed by Billio et al (2012) and Diebold and Yilmaz (2014), who employ Granger-causality tests and variance decompositions. Their methodology has been extended by Ahelegbey et al (2016) and Giudici and Spelta (2016) who introduced stochastic correlation networks. Another relevant reference consists in Das (2015), who derives a risk decomposition into individual and network (contagion) contributions.…”

“…Specifically, we extend (a) the approach of Ahelegbey et al (2016) by adding non-directed graphical Gaussian models based on partial correlations into their graphical vector autoregressive; (b) the approach of Giudici and Spelta (2016), improving their symmetric graphical Gaussian models with an autoregressive component derived through a VAR model; (c) the approach of Das (2015), by augmenting it with a probabilistic decomposition of risks into individual and contagion components. A further contribution of this paper consists in the extension of the application domain of correlation networks.…”

Are Corporate Bond Defaults Contagious across Sectors?

“…Diebold and Yılmaz (2014) also propose a variety of connectedness measures based on variance decompositions that can be used to track time-varying connectedness of stock return volatilities. Ahelegbey et al (2016) present an innovative Bayesian graphical approach to identification in vector autoregressive (VAR) models, finding strong unidirectional linkage from financial to non-financial sectors during the recent financial crisis and bidirectional linkages during the European sovereign debt crisis. However, it is unclear whether these linkages represent contagion per se, or more normal shock transmission.…”