协整，单整不太懂，只是觉得单位根检验很好用。

I have not encountered with such problems so I cannot give you a very presice answer. However, I have find a good paper perfectly having the content you want. It is a little hard to read, but it is worth reading since you are to handle such a special problem. For simplicity, I think EG 2-step test works though it has not a very high power.

Hope it will help you. Good luck.