Rank-based diagnostics for the integration order of a VAR solution
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Representation theorems of (co)integrated processes - in the wake of Granger’s seminal work and Johansen’s key contributions and up to the recent Faliva and Zoia’s analysis within a rigorous and intriguing algebraic framework - have traced the road map of time-series econometrics. This paper, further developing Faliva and Zoia‘s approach to the derivation of representation theorems (2002 a,b; 2003), sheds new light onto the intriguing mechanism linking the coefficient matrices of the VAR-polynomial expansion about a unit root, with the integration order of the out- coming process. Indeed an elegant rank criterion is established which, in turn, leads to an enlightening flow-chart representation of coefficient-matrix ranks versus integration order interlacement. Finally, Faliva and Zoia’s unified representation theorem (2003) can be given a smart new formulation.
Keywords: VAR models, Integration order, Laurent expansion, Rank criterion. Author biographyMaria Grazia Zoia, Istituto di Econometria e Matematica, Università Cattolica di Milano (e-mail: Maria.Zoia@unicatt.it). |
