Granger Causal Priority and Choice of Variables in Vector Autoregressions

摘要

We derive a closed-form expression for the posterior probability of Granger noncausality in a gaussian vector autoregression with a conjugate prior. We also express in closed form the posterior probability of Granger causal priority, a more general relation that accounts for indirect effects between variables and therefore is suitable in a multivariate context. One can use these results to answer the classic question, Is variable z relevant for variable x? and to choose variables for a vector autoregression.