threshold unit roots???

[zabiah]

I am trying to apply Hansen's threshold model (1996) in a VAR context. Inferences in that model require the DGP to be covariance stationary. I have conducted a battery of tests for unit roots especially for inflation during 1985-2010. ADF, PP have conflicting answers. Structural break type unit roots tests don't really make a lot of sense during the data period that I am considering (1985-2010). Any hint will be great.

I just do not want to difference the series if I really don't have to as it may dilute the threshold effects in the VAR: the thing I want to analyze at the first place.