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Granger's representation theorem: A closed-form expression for I(1) processes

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  • Peter Reinhard Hansen

Abstract

The Granger representation theorem states that a cointegrated vector autoregressive process can be decomposed into four components: a random walk, a stationary process, a deterministic part, and a term that depends on the initial values. In this paper, we present a new proof of the theorem. This proof enables us to derive closed-form expressions of all terms of the representation and allows a unified treatment of models with different deterministic specifications. The applicability of our results is illustrated by examples. For example, the closed-form expressions are useful for impulse response analyses and facilitate the analysis of cointegration models with structural changes. Copyright 2005 Royal Economic Society

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Bibliographic Info

Article provided by Royal Economic Society in its journal The Econometrics Journal.

Volume (Year): 8 (2005)
Issue (Month): 1 (03)
Pages: 23-38

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Handle: RePEc:ect:emjrnl:v:8:y:2005:i:1:p:23-38

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Cited by:
  1. Adolfson, Malin & Laséen, Stefan & Lindé, Jesper & Villani, Mattias, 2007. "Evaluating An Estimated New Keynesian Small Open Economy Model," CEPR Discussion Papers 6027, C.E.P.R. Discussion Papers.
  2. Òscar Jordà, 2005. "Estimation and Inference of Impulse Responses by Local Projections," American Economic Review, American Economic Association, vol. 95(1), pages 161-182, March.
  3. Maria Grazia Zoia, 2006. "A New Algebra ic Approach to Representation Theorems for (Co)integrated Processes up to the Second Order," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 2006.06, Institut d'Economie et Econométrie, Université de Genève.
  4. Niklas Ahlgren & Mikael Juselius, 2012. "Tests for cointegration rank and the initial condition," Empirical Economics, Springer, vol. 42(3), pages 667-691, June.
  5. Alexander Chudik & Vanessa Smith, 2013. "The GVAR approach and the dominance of the U.S. economy," Globalization and Monetary Policy Institute Working Paper 136, Federal Reserve Bank of Dallas.
  6. Paruolo Paolo, 2005. "Design of vector autoregressive processes for invariant statistics," Economics and Quantitative Methods qf0504, Department of Economics, University of Insubria.
  7. Juselius , Mikael & Kim, Moshe & Ringbom, Staffan, 2009. "Do markup dynamics reflect fundamentals or changes in conduct?," Research Discussion Papers 12/2009, Bank of Finland.

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