Threshold cointegration and stationary data

[Roger&Young]

Hi.
I am trying threshold cointegration for income and revenue relationship, using technique by Enders and Siklos(2001) (of course, and by Enders and Granger(1998)).
But I found something that I can not understand from the paper and other papers by Enders and someone else using the same technique.
They all skip unit-root test for data in the papers!
I think that all data must have unit root for cointegration relationship to exist among them. Is it wrong? Or threshold cointegration tech by Enders and Siklos(2001) does not need its data to have unit root? So we can just skip unit root test (ex, ADF test or KPSS test) to perform threshold cointegration test? We don't need to care if data are stationary or have unit roots here?
Some papers using the same technique by others performed unit root test before they performed threshold cointegration test. I saw the papers.
BUT some other papers by Enders and other guys just skipped unit root test for the data.
Which is right?
Someone kindly tell me, please.

:D