VAR Cointegration in VARMA Models
The method for estimation and testing for cointegration put forward by Johansen assumes that the data are described by a vector autoregressive process. In this article we extend the data generating process to autoregressive moving average models without unit roots in the MA polynomial. We first extend some matrix algebraic relationships for I(1) processes and derive their implications for the structure theory of cointegration. Specifically we show that the cointegrating space is invariant to MA errors which have no unit roots in the MA polynomial. The above results permit to prove the robustness of the Johansen estimates of the cointegrating space in a Gaussian vector autoregressive framework when the true model is vector autoregressive moving average, without unit roots in the MA polynomial. The small sample properties of the theoretical results are examined through a small simulation study.
|Date of creation:||May 1999|
|Contact details of provider:|| Postal: Josefstädterstr. 39, A-1080 Vienna, Austria|
Phone: ++43 - (0)1 - 599 91 - 0
Fax: ++43 - (0)1 - 599 91 - 555
Web page: http://www.ihs.ac.at
More information through EDIRC
|Order Information:|| Postal: Institute for Advanced Studies - Library, Josefstädterstr. 39, A-1080 Vienna, Austria|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Toda, Hiro Y., 1995. "Finite Sample Performance of Likelihood Ratio Tests for Cointegrating Ranks in Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1015-1032, October.
- Bierens, Herman J., 1997.
"Nonparametric cointegration analysis,"
Journal of Econometrics,
Elsevier, vol. 77(2), pages 379-404, April.
- Bierens, H.J., 1995. "Nonparametric cointegration analysis," Discussion Paper 1995-123, Tilburg University, Center for Economic Research.
- Ronald Bewley & Minxian Yang, 1998. "On The Size And Power Of System Tests For Cointegration," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 675-679, November.
- Bewley, R. & Yang, M., 1996. "On the Size and Power of System Tests for Cointegration," Papers 96/9, New South Wales - School of Economics.
- Haldrup, Niels & Salmon, Mark, 1998. "Representations of I(2) cointegrated systems using the Smith-McMillan form," Journal of Econometrics, Elsevier, vol. 84(2), pages 303-325, June.
- Podivinsky, Jan M., 1998. "Testing misspecified cointegrating relationships," Economics Letters, Elsevier, vol. 60(1), pages 1-9, July. Full references (including those not matched with items on IDEAS)