The Wold Representation, Degree of Non-Cointegration, and the Johansen Trace Test

The empirical size and power properties of the Johansen vector autoregression based trace test for cointegration are considered in the case where the data is generated by a sequence of vector moving average processes with declining degrees of non-cointegration. Rejection frequencies are sensitive to the trade off between degrees of freedom in estimation and how well the fitted VAR model approximates the underlying VMA. Conventional null distributions can provide a poor basis for inference in this situation