Cointegration, Root Functions and Minimal Bases

Massimo Franchi and Paolo Paruolo

Econometrics, 2021, vol. 9, issue 3, 1-27

Abstract: This paper discusses the notion of cointegrating space for linear processes integrated of any order. It first shows that the notions of (polynomial) cointegrating vectors and of root functions coincide. Second, it discusses how the cointegrating space can be defined (i) as a vector space of polynomial vectors over complex scalars, (ii) as a free module of polynomial vectors over scalar polynomials, or finally (iii) as a vector space of rational vectors over rational scalars. Third, it shows that a canonical set of root functions can be used as a basis of the various notions of cointegrating space. Fourth, it reviews results on how to reduce polynomial bases to minimal order—i.e., minimal bases. The application of these results to Vector AutoRegressive processes integrated of order 2 is found to imply the separation of polynomial cointegrating vectors from non-polynomial ones.

Keywords: VAR; cointegration; I(d); vector spaces (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Related works:
Working Paper: Cointegration, root functions and minimal bases (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jecnmx:v:9:y:2021:i:3:p:31-:d:615763

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