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Cointegration and Error Correction Mechanisms

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  • Hylleberg, Svend
  • Mizon, Grayham E

Abstract

Starting from a multivariate Wold representation for N variables that are integrated of order 1, this paper shows that, given that the N variables have r cointegrating vectors, there is an equivalence between five alternative representations of the multivariate model: the autoregressive representation; the error-correction representation; the interim multiplier representation; the Bewley (1979) representation; and the common trend representation. Proof of the theorem uses a result based on the Smith-McMillan lemma for polynomial matrices. The paper concludes by commenting on the different representations. Copyright 1989 by Royal Economic Society.

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Bibliographic Info

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

Volume (Year): 99 (1989)
Issue (Month): 395 (Supplement)
Pages: 113-25

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Handle: RePEc:ecj:econjl:v:99:y:1989:i:395:p:113-25

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Cited by:
  1. David F. Hendry & Neil R. Ericsson, 1990. "Modeling the demand for narrow money in the United Kingdom and the United States," International Finance Discussion Papers 383, Board of Governors of the Federal Reserve System (U.S.).
  2. Anthony Garratt & Gary Koop & Emi Mise & Shaun Vahey, 2008. "Real-time Prediction with UK Monetary Aggregates in the Presence of Model Uncertainty," Reserve Bank of New Zealand Discussion Paper Series DP2008/13, Reserve Bank of New Zealand.
  3. Escribano, Alvaro & Pfann, Gerard A., 1998. "Non-linear error correction, asymmetric adjustment and cointegration," Economic Modelling, Elsevier, vol. 15(2), pages 197-216, April.
  4. Ericsson, Neil R., 1992. "Cointegration, exogeneity, and policy analysis: An overview," Journal of Policy Modeling, Elsevier, vol. 14(3), pages 251-280, June.
  5. Podivinsky, Jan M., 1998. "Testing misspecified cointegrating relationships," Economics Letters, Elsevier, vol. 60(1), pages 1-9, July.
  6. Uwe Hassler & Jürgen Wolters, 2006. "Autoregressive distributed lag models and cointegration," AStA Advances in Statistical Analysis, Springer, vol. 90(1), pages 59-74, March.
  7. Su Zhou, 1998. "Exchange rate systems and linkages in the pacific basin," Atlantic Economic Journal, International Atlantic Economic Society, vol. 26(1), pages 66-84, March.
  8. James H. Stock & Mark W. Watson, 1989. "A Simple MLE of Cointegrating Vectors in Higher Order Integrated Systems," NBER Technical Working Papers 0083, National Bureau of Economic Research, Inc.
  9. Fragiskos Archontakis, 1998. "An alternative proof of Granger’s Representation Theorem forI(1) systems through Jordan matrices," Statistical Methods and Applications, Springer, vol. 7(2), pages 111-127, August.
  10. Chen, Sheng-Syan & Lee, Cheng-few & Shrestha, Keshab, 2003. "Futures hedge ratios: a review," The Quarterly Review of Economics and Finance, Elsevier, vol. 43(3), pages 433-465.
  11. Heejoon Kang, 1999. "The Applied Cointegration Analysis for the Open Economy: A Critical Review," Open Economies Review, Springer, vol. 10(3), pages 325-346, July.
  12. Kumah, F.Y., 1997. "Common Stochastic Trends and Policy Shocks in the Open Economy: Empirical Essays in International Finance and Monetary Policy," Open Access publications from Tilburg University urn:nbn:nl:ui:12-74321, Tilburg University.
  13. Rahman, Mizanur, 2008. "The Impact of a Common Currency on East Asian Production Networks and China’s Exports Behavior," MPRA Paper 13931, University Library of Munich, Germany.
  14. van Tol, Michel R & Wolff, Christian C, 2005. "Forecasting the Spot Exchange Rate with the Term Structure of Forward Premia: Multivariate Threshold Cointegration," CEPR Discussion Papers 4958, C.E.P.R. Discussion Papers.
  15. Hendry, David F., 2000. "On detectable and non-detectable structural change," Structural Change and Economic Dynamics, Elsevier, vol. 11(1-2), pages 45-65, July.
  16. Lyhagen, Johan, 1998. "Maximum likelihood estimation of the multivariate fractional cointegrating model," Working Paper Series in Economics and Finance 233, Stockholm School of Economics.
  17. John Pippenger, 1991. "Forward rates as predictors of future spot rates in small open economies: The case of Kuwait," Open Economies Review, Springer, vol. 2(2), pages 183-201, June.

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