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A New Algebra ic Approach to Representation Theorems for (Co)integrated Processes up to the Second Order

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Author Info
Maria Grazia Zoia
Abstract

The paper establishes a unified representation theorem for (co)integrated processes up to the second order which provides a compact and informative insight into the solution of VAR models with unit roots, and sheds light on the cointegration features of the engendered processes. The theorem is primarily stated by taking a one-lag specification as a reference frame, and it is afterwards extended to cover the case of an arbitrary number of lags via a companion-form based approach. All proofs are obtained by resorting to an innovative and powerful algebraic apparatus tailored to the derivation of the intended results.

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Publisher Info
Paper provided by Département d'Econométrie, Université de Genève in its series Cahiers du Département d'Econométrie with number 2006.06.

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Length: 20 pages
Date of creation: Oct 2006
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Handle: RePEc:gen:geneem:2006.06

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Keywords: Unified representation theorem Cointegration Orthogonal-complement algebra Laurent expansion in matrix form

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  1. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March. [Downloadable!] (restricted)
  2. repec:cup:etheor:v:8:y:1992:i:2:p:188-202 is not listed on IDEAS
  3. Peter Reinhard Hansen, 2005. "Granger's representation theorem: A closed-form expression for I(1) processes," Econometrics Journal, Royal Economic Society, vol. 8(1), pages 23-38, 03. [Downloadable!] (restricted)
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