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VARs, Cointegration and Common Cycle Restrictions

  • Heather M Anderson


  • Farshid Vahid


This paper argues that VAR models with cointegration and common cycles can be usefully viewed as observable factor models. The factors are linear combinations of lagged levels and lagged differences, and as such, these observable factors have potential for forecasting. We illustrate this forecast potential in both a Monte Carlo and empirical setting, and demonstrate the difficulties in developing forecasting "rules of thumb" for forecasting in multivariate systems.

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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 14/10.

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Length: 50 pages
Date of creation: May 2010
Date of revision:
Handle: RePEc:msh:ebswps:2010-14
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  1. Daniel F. Waggoner & Tao Zha, 1998. "Conditional forecasts in dynamic multivariate models," FRB Atlanta Working Paper 98-22, Federal Reserve Bank of Atlanta.
  2. Hoffman, Dennis L & Rasche, Robert H, 1996. "Assessing Forecast Performance in a Cointegrated System," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(5), pages 495-517, Sept.-Oct.
  3. Elliott, Graham, 2006. "Forecasting with Trending Data," Handbook of Economic Forecasting, Elsevier.
  4. LeSage, James P, 1990. "A Comparison of the Forecasting Ability of ECM and VAR Models," The Review of Economics and Statistics, MIT Press, vol. 72(4), pages 664-71, November.
  5. Heather M. Anderson & Chin Nam Low & Ralph Snyder, 2004. "Single Source of Error State Space Approach to the Beveridge Nelson Decomposition," Monash Econometrics and Business Statistics Working Papers 21/04, Monash University, Department of Econometrics and Business Statistics.
  6. Athanasopoulos, George & Guillen, Osmani Teixeira Carvalho & Issler, João Victor, 2009. "Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions," Economics Working Papers (Ensaios Economicos da EPGE) 688, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  7. Aznar, Antonio & Salvador, Manuel, 2002. "Selecting The Rank Of The Cointegration Space And The Form Of The Intercept Using An Information Criterion," Econometric Theory, Cambridge University Press, vol. 18(04), pages 926-947, August.
  8. Boriss Siliverstovs & Tom Engsted & Niels Haldrup, 2003. "Long-Run Forecasting in Multicointegrated Systems," Discussion Papers of DIW Berlin 381, DIW Berlin, German Institute for Economic Research.
  9. Shoesmith, Gary L., 1995. "Multiple cointegrating vectors, error correction, and forecasting with Litterman's model," International Journal of Forecasting, Elsevier, vol. 11(4), pages 557-567, December.
  10. 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.
  11. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 369-80, October.
  12. Christopher A. Sims & Tao Zha, 1996. "Bayesian methods for dynamic multivariate models," FRB Atlanta Working Paper 96-13, Federal Reserve Bank of Atlanta.
  13. Mackinnon, J.G. & Haug, A.A. & Michelis, L., 1996. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," G.R.E.Q.A.M. 96a09, Universite Aix-Marseille III.
  14. Christoffersen, Peter F & Diebold, Francis X, 1998. "Cointegration and Long-Horizon Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 450-58, October.
  15. Hendry, David F. & Massmann, Michael, 2007. "Co-Breaking: Recent Advances and a Synopsis of the Literature," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 33-51, January.
  16. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1986. "Forecasting and conditional projection using realistic prior distribution," Staff Report 93, Federal Reserve Bank of Minneapolis.
  17. Chao, John C. & Phillips, Peter C. B., 1999. "Model selection in partially nonstationary vector autoregressive processes with reduced rank structure," Journal of Econometrics, Elsevier, vol. 91(2), pages 227-271, August.
  18. Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-60, Oct.-Dec..
  19. Pesaran, M. Hashem & Timmermann, Allan, 2007. "Selection of estimation window in the presence of breaks," Journal of Econometrics, Elsevier, vol. 137(1), pages 134-161, March.
  20. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  21. Michael P. Clements & David F. Hendry, 2002. "Modelling methodology and forecast failure," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 319-344, 06.
  22. Kadiyala, K. Rao & Karlsson, Sune, 1994. "Numerical Aspects of Bayesian VAR-modeling," SSE/EFI Working Paper Series in Economics and Finance 12, Stockholm School of Economics.
  23. Gary Koop & Roberto León-González & Rodney W. Strachan, 2005. "Efficient Posterior Simulation for Cointegrated Models with Priors On the Cointegration Space," Discussion Papers in Economics 05/13, Department of Economics, University of Leicester, revised Apr 2006.
  24. Hecq, Alain & Palm, Franz C. & Urbain, Jean-Pierre, 2006. "Common cyclical features analysis in VAR models with cointegration," Journal of Econometrics, Elsevier, vol. 132(1), pages 117-141, May.
  25. Engle, Robert F. & Yoo, Byung Sam, 1987. "Forecasting and testing in co-integrated systems," Journal of Econometrics, Elsevier, vol. 35(1), pages 143-159, May.
  26. Anderson, Heather M. & Vahid, Farshid, 1998. "Testing multiple equation systems for common nonlinear components," Journal of Econometrics, Elsevier, vol. 84(1), pages 1-36, May.
  27. Gonzalo, Jesus & Pitarakis, Jean-Yves, 1998. "Specification via model selection in vector error correction models," Economics Letters, Elsevier, vol. 60(3), pages 321-328, September.
  28. Vahid, Farshid & Issler, Joao Victor, 2002. "The importance of common cyclical features in VAR analysis: a Monte-Carlo study," Journal of Econometrics, Elsevier, vol. 109(2), pages 341-363, August.
  29. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  30. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, December.
  31. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 393-95, October.
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