A Bayesian Approach to Modelling Graphical Vector Autoregressions

Abstract

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Bayesian Graphical Models for STructural Vector Autoregressive Processes

“…This challenge has been discussed extensively as a model determination problem (see Chickering et al , ; Corander and Villani, ). However, we follow the Bayesian paradigm of Madigan and York (), Giudici and Green () and Dawid and Lauritzen (), which allows us to take into account structure and parameter uncertainty.…”

“…In this paper, we propose an identification approach for SVAR models based on a graph representation of the conditional independence among variables (see Pearl, ; Lauritzen and Wermuth, ; Whittaker, ; Wermuth and Lauritzen, ). The graph inference discussed in this paper is in the spirit of Corander and Villani (), but differs substantially from it. A first relevant difference is that our approach considers acyclic graphs, whereas in Corander and Villani () the dependence structures are not acyclic and cannot be used to achieve identification.…”

“…The graph inference discussed in this paper is in the spirit of Corander and Villani (), but differs substantially from it. A first relevant difference is that our approach considers acyclic graphs, whereas in Corander and Villani () the dependence structures are not acyclic and cannot be used to achieve identification. A second major difference is that we propose a joint inference of the graphs and the parameters, whereas they focus only on the causal structures.…”

“…A second major difference is that we propose a joint inference of the graphs and the parameters, whereas they focus only on the causal structures. Furthermore, Corander and Villani () apply a fractional Bayes approach, which is a questionable methodology for a variety of models (see, for example, Berger and Pericchi, ; de Santis and Spezzaferri, deSantis and Spezzaferri). Finally, it is not at all clear in general, how one should define the factorization of the likelihood, or which fractions should be used for each component.…”

Bayesian Graphical Model Application for Monetary Policy and Macroeconomic Performance in Nigeria

“…Our intention is to combine BGN with SVAR, in order to examine interrelationship among monetary policies and macroeconomic performances in Nigeria. However, many previous studies have worked on causal inference using BGN-SVAR in developed countries, studies like Swanson and Granger [11], Demiralp and Hoover [9], Moneta and Spirites [12], Corander and Villani [13] and more recently Ahelegbey et al [6]. The advantage of the BGN-SVAR is that causal influences are tracked down among variables of interest either instantaneously or with time lags using conditional probabilistic inference on the structural model.…”