AStA Advances in Statistical Analysis

, Volume 97, Issue 3, pp 287–295 | Cite as

Codependent VAR models and the pseudo-structural form

  • Carsten Trenkler
  • Enzo Weber
Original Paper


This paper investigates whether codependence restrictions can be uniquely imposed on VAR models via the so-called pseudo-structural form used in the literature. Codependence of order q is given if a linear combination of autocorrelated variables eliminates the serial correlation after q lags. Importantly, maximum likelihood estimation and likelihood ratio testing are only possible if the codependence restrictions can be uniquely imposed. Applying the pseudo-structural form, our study reveals that this is not generally the case, but that unique imposition is guaranteed in several important special cases.


Codependence VAR Pseudo-structural form  Serial correlation common features 



We are grateful to two anonymous referees, the editor, Kyusang Yu and participants of seminars at the Central Bank Norway, the Humboldt University Berlin, the Leibniz University Hannover, and the University of Mannheim for very helpful comments. Of course, all remaining errors are our own.


  1. Cubadda, G., Hecq, A.: On non-contemporaneous short-run comovements. Econ. Lett. 73, 389–397 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  2. Engle, R.F., Kozicki, S.: Testing for common features. J. Bus. Econ. Stat. 11, 369–380 (1993)Google Scholar
  3. Franchi, M., Paruolo, P.: A characterization of vector autoregressive processes with common cyclical features. J. Econom. 163, 105–117 (2011)MathSciNetCrossRefGoogle Scholar
  4. Gourieroux, C., Peaucelle, I.: (1988) Detecting a long-run relationship (with an application to the P.P.P. hypothesis). Working Paper 8902, CREMAPGoogle Scholar
  5. Gourieroux, C., Peaucelle, I.: Series codependantes: application a l’hypothese de parité du pouvoir d’achat. Rev. d’Analyse Economique 68, 283–304 (1992)Google Scholar
  6. Lütkepohl, H.: New Introduction to Multiple Time Series Analysis. Springer, Berlin (2005)zbMATHCrossRefGoogle Scholar
  7. Paruolo, P.: (2003) Common dynamics in I(1) VAR systems. Discussion Paper 2003/35. Department of Economics, University of InsubriaGoogle Scholar
  8. Schleicher, C.: Codependence in cointegrated autoregressive models. J. Appl. Econom. 22, 137–159 (2007)MathSciNetCrossRefGoogle Scholar
  9. Tiao, G.C., Tsay, R.S.: Model specification in multivariate time series (with discussion). J. R. Stat. Soc. Ser. B 51, 157–213 (1989)MathSciNetzbMATHGoogle Scholar
  10. Trenkler, C., Weber, E.: (2012) Codependent VAR models and the pseudo-structural form. Working Paper ECON 12-10. Department of Economics, University of MannheimGoogle Scholar
  11. Trenkler, C., Weber, E.: Testing for codependence of non-stationary variables. Appl. Econ. 45, 1953–1964 (2013)CrossRefGoogle Scholar
  12. Vahid, F., Engle, R.F.: Common trends and common cycles. J. Appl. Econom. 8, 341–360 (1993)Google Scholar
  13. Vahid, F., Engle, R.F.: Codependent cycles. J. Econom. 80, 199–221 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  14. Vahid, F., Issler, J.V.: The importance of common cyclical features in VAR analysis: a Monte-Carlo study. J. Econom. 109, 341–363 (2002)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of MannheimMannheimGermany
  2. 2.Department of Economics and Econometrics University of RegensburgRegensburgGermany
  3. 3.Institute of Employment ResearchNurembergGermany

Personalised recommendations