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The sampling properties of conditional independence graphs for I (1) structural VAR models
Author(s) -
Wilson Granville Tunnicliffe,
Reale Marco
Publication year - 2008
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2008.00583.x
Subject(s) - mathematics , conditional independence , autoregressive model , series (stratigraphy) , independence (probability theory) , directed acyclic graph , vector autoregression , inference , econometrics , asymptotic distribution , sampling distribution , graph , statistics , discrete mathematics , algorithm , computer science , artificial intelligence , paleontology , estimator , biology
. 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.