Testing for cointegration in the presence of mis-specified structural change

The finite-sample properties of cointegration tests incorporating structural change are derived when applied to independent unit root processes subject to changes in innovation variance. It is shown that decreases in innovation variance can result in severe size distortion, with the extent of spurious rejection dependent upon which series experiences a break and when the break occurs. Mis-specified structural change is therefore shown to result in spurious regression, the very problem cointegration analysis attempts to overcome.