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The sampling properties of conditional independence graphs for I(1) structural VAR models

Abstract.  Structural vector autoregressions allow dependence among contemporaneous variables. If such models have a recursive structure, the relationships among the variables can be represented by directed acyclic graphs. The identification of these relationships for stationary series may be enabled by the examination of the conditional independence graph constructed from sample partial autocorrelations of the observed series. In this article, we extend this approach to the case when the series follows an I(1) vector autoregression. For such a model, estimated regression coefficients may have non‐standard asymptotic distributions and in small samples this affects the distribution of sample partial autocorrelations. We show that, nevertheless, in large samples, exactly the same inference procedures may be applied as in the stationary case.