Journal of the Italian Statistical Society

, Volume 7, Issue 2, pp 111–127 | Cite as

An alternative proof of Granger’s Representation Theorem forI(1) systems through Jordan matrices

  • Fragiskos Archontakis


The Jordan form of the VAR’s companion matrix is used for proving the equivalence between the statement that there are no Jordan blocks of order two or higher and the condition of Granger’s Representation Theorem for anI(1) series. Furthermore, a diagonal polynomial matrix containing the unit roots associated to the VAR system is derived and related to the Granger’s Representation Theorem.


VAR Systems Integrated Series Granger’s Representation Jordan matrices 


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Copyright information

© Società Italiana di Statistica 1998

Authors and Affiliations

  1. 1.Department of EconomicsEuropean University InstituteFirenzeItaly

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