Cointegration, root functions and minimal bases

Massimo Franchi and Paolo Paruolo

No 2019/2, DSS Empirical Economics and Econometrics Working Papers Series from Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome

Abstract: This paper discusses the concept of cointegrating space for systems integrated of order higher than 1. It is first observed that the notions of (polynomial) cointegrating vectors and of root functions coincide. Second, the cointegrating space is defined as a subspace of the space of rational vectors. Third, it is shown that canonical sets of root functions can be used to generate a basis of the cointegrating space. Fourth, results on how to reduce bases of rational vector spaces to polynomial bases with minimal order (i.e. minimal bases) are shown to imply the separation of cointegrating vectors that potentially do not involve differences of the process from the ones that require them. Finally, it is argued that minimality of polynomial bases and economic identification of cointegrating vectors can be properly combined.

Keywords: VAR; Cointegration; I(d); Vector spaces. (search for similar items in EconPapers)
JEL-codes: C12 C33 C55 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2019-12
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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http://www.dss.uniroma1.it/RePec/sas/wpaper/20192_FP.pdf First version, 2019 (application/pdf)

Related works:
Journal Article: Cointegration, Root Functions and Minimal Bases (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:sas:wpaper:20192

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