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Biometrika 2002 89(2):457-461; doi:10.1093/biomet/89.2.457
© 2002 by Biometrika Trust
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The sampling properties of conditional independence graphs for structural vector autoregressions

Marco Reale1 and Granville Tunnicliffe Wilson2

1 Department of Mathematics and Statistics, University of Canterbury, PB 4800 Christchurch, New Zealand m.reale@math.canterbury.ac.nz 2 Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, U.K.g.tunnicliffe-wilson@lancaster.ac.uk

Structural vector autoregressions allow contemporaneous series dependence and assume errors with no contemporaneous correlation. Models of this form, that also have a recursive structure, can be described by a directed acyclic graph.An important tool for identification of these models is the conditional independence graph constructed from the contemporaneous and lagged values of the process. We determine the large-sample properties of statistics used to test for the presence of links in this graph. A simple example illustrates how these results may be applied.

Key Words: Causality; Moralisation; Partial correlation

Received August 2000. Revised November 2001


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