Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/247621
Authors: 
Franchi, Massimo
Paruolo, Paolo
Year of Publication: 
2021
Citation: 
[Journal:] Econometrics [ISSN:] 2225-1146 [Volume:] 9 [Year:] 2021 [Issue:] 3 [Pages:] 1-27
Publisher: 
MDPI, Basel
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.
Subjects: 
cointegration
I(d)
VAR
vector spaces
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article

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