This paper discusses inference in self exciting threshold autoregressive (SETAR)models, where there is a number of inference problems that have not been resolved so far. Of main interest is inference for the threshold parameter. The asymptotics of the corresponding estimator strongly depend upon whether the SETAR model is continuous or discontinuous, going from a normal distribution to a non-standard distribution with many nuisance parameters that can not be consistently estimated. This makes standard inference impossible. We show valid inference can be drawn by the use of the subsampling method, even when the type of continuity is unknown. As a by product we show how to test for the continuity of the SETAR model. The good small sample performance of the methods is illustrated via some simulation studies.