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

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Summary

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.

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Authors and Affiliations

  1. Department of Economics, European University Institute, Via dei Roccettini 9-I-50016, San Domenico di Fiesole, Firenze, Italy

    Fragiskos Archontakis

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  1. Fragiskos Archontakis
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Correspondence to Fragiskos Archontakis.

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This work is part of my Ph.D. thesis under the guidance of Søren Johansen. His comments along with those of the two anonymous referees have greatly improved the content and the presentation of the paper.

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Archontakis, F. An alternative proof of Granger’s Representation Theorem forI(1) systems through Jordan matrices. J. Ital. Statist. Soc. 7, 111–127 (1998). https://doi.org/10.1007/BF03178924

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