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|
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- Bierens, Herman J., 1997.
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- 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.
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