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NECESSARY AND SUFFICIENT CONDITIONS FOR CAUSALITY TESTING IN MULTIVARIATE ARMA MODELS
Author(s) -
Kang Heejoon
Publication year - 1981
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.1467-9892.1981.tb00315.x
Subject(s) - mathematics , multivariate statistics , matrix (chemical analysis) , causality (physics) , parametric statistics , granger causality , zero (linguistics) , econometrics , statistics , linguistics , materials science , physics , philosophy , quantum mechanics , composite material
. The necessary and sufficient conditions for Granger causality are provided. The condition is that some linear combinations of certain elements of AR matrix and certain elements of MA matrix must vanish. It is less restrictive than the condition heretofore utilized in the literature which is only sufficient in which certain elements in AR matrix as well as certain elements in MA matrix themselves are zero. A proper parsimonious parametric test procedure is also established by using the necessary and sufficient condition.