Gregoir, Stéphane (1999) Multivariate Time Series with Various Hidden Unit Roots: Part I : Integral Operator Algebra and Representation Theory. Econometric Theory, vol. 15 (n° 4). pp. 435-468.

Abstract

Following the approach proposed by Gregoir and Laroque (1993, Econometric Theory 9, 329–342), we consider a class of multivariate processes that, when differenced enough, yields covariance stationary processes whose determinant of the matrix series associated with their Wold representation has various unit roots with various orders of multiplicity we restrict to be integers. A representation theorem is provided that involves different polynomial error correction terms at each frequency associated with each unit root. An identification criterion for each set of error correction terms is proposed