Abstract

The notion of causality in multiple time series is addressed from a Bayesian graphical modelling perspective in the class of vector autoregressive (VAR) processes. Due to the very large number of graph structures that may be considered, simulation based inference, such as Markov chain Monte Carlo, is not feasible. Therefore, we derive an approximate joint posterior distribution of the number of lags in the autoregression and the causality structure represented by graphs using a fractional Bayes approach. Some properties of the approximation are derived and the analysis is illustrated on a four-dimensional macroeconomic system and five-dimensional air pollution data.

Keywords: Causality, Fractional Bayes, graphical models, lag length selection, vector autoregression.