The sampling properties of conditional independence graphs for structural vector autoregressions

REALE, MARCO
WILSON, GRANVILLE TUNNICLIFFE

Department of Mathematics and Statistics, University of Canterbury, PB 4800 Christchurch, New Zealand. [email protected] (REALE)
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, U.K. [email protected] (WILSON)

[Received August 2000. Revised November 2001]

Biometrika 89(2):p 457-461, June 2002.

SUMMARY

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.