Title: A general inversion theorem for cointegration
Citation: ECONOMETRIC REVIEWS vol. 38 no. 10 p. 1176-1201
Publication Year: 2019
JRC N°: JRC107018
ISSN: 0747-4938 (online)
URI: https://publications.jrc.ec.europa.eu/repository/handle/JRC107018
DOI: 10.1080/07474938.2018.1536100
Type: Articles in periodicals and books
Abstract: A generalization of the Granger and the Johansen Representation Theorems valid for any (possibly fractional) order of integration is presented. This Representation Theorem is based on inversion results that characterize the order of the pole and the coefficients of the Laurent series representation of the inverse of a matrix function around a singular point. Explicit expressions of the matrix coefficients of the (polynomial) cointegrating relations, of the Common Trends and of the Triangular representations are provided, either starting from the Moving Average or the Auto Regressive form. This contribution unifies different approaches in the literature and extends them to an arbitrary order of integration. The role of deterministic terms is discussed in detail.
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