Article ; Online: Cointegration, Root Functions and Minimal Bases
Econometrics, Vol 9, Iss 31, p
2021 Volume 31
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 ... ...
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. |
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Keywords | VAR ; cointegration ; I(d) ; vector spaces ; Economics as a science ; HB71-74 |
Language | English |
Publishing date | 2021-08-01T00:00:00Z |
Publisher | MDPI AG |
Document type | Article ; Online |
Database | BASE - Bielefeld Academic Search Engine (life sciences selection) |
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