A generalization of the Granger and the Johansen Representation Theorems valid for any (possibly fractional) order of integration is pre- sented. 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) cointe- grating relations, of the Common Trends and of the Triangular representa- tions are provided, either starting from the Moving Average or the Auto Regressive form. This contribution unifies different approaches in the litera- ture and extends them to an arbitrary order of integration. The role of deterministic terms is discussed in detail.
A general inversion theorem for cointegration / Franchi, Massimo; Paruolo, Paolo. - In: ECONOMETRIC REVIEWS. - ISSN 0747-4938. - 38:10(2019), pp. 1176-1201. [10.1080/07474938.2018.1536100]
A general inversion theorem for cointegration
Franchi, Massimo;
2019
Abstract
A generalization of the Granger and the Johansen Representation Theorems valid for any (possibly fractional) order of integration is pre- sented. 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) cointe- grating relations, of the Common Trends and of the Triangular representa- tions are provided, either starting from the Moving Average or the Auto Regressive form. This contribution unifies different approaches in the litera- ture and extends them to an arbitrary order of integration. The role of deterministic terms is discussed in detail.File | Dimensione | Formato | |
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