Cointegration in singular ARMA models

- We consider I(1) ARMA processes with singular error covariance matrix.
- Also in the left coprime case the cointegrating rank shown to depend upon a(1) only.
- Definition and discussion of exact cointegration.

We consider the cointegration properties of singular ARMA processes integrated of order one. Such processes are necessarily cointegrated as opposed to the regular case. We show that in the left coprime case the cointegrating space only depends upon the autoregressive polynomial at one.