Testing for cointegration in I(1) state space systems via a finite order approximation

The present paper employs the infinite order error correction representation of the observables of a I(1) state space system and analyzes by simulation the small sample behaviour of the test on rank and on the cointegrating vectors calculated via a finite order cointegrated vector autoregressive approximation. The rank test performs very well in systems with a small number of states and stochastic trends (≤4) and a medium number of observables (≤35) already for a sample of size T = 300 and it is still reliable with a large number of observables (≤140) when T = 600. The behaviour of the test on the cointegrating vectors is more problematic.