This paper develops an asymptotic theory of inference for a two-regime threshold autoregressive (TAR) model with an autoregressive root which is local-to-unity. We find that the asymptotic null distribution of the Wald test for a threshold is non-standard and mildly dependent on the...

A distribution theory is developed for least squares estimates of the threshold in threshold autoregressive (TAR) models. We find that if we let the threshold effect (the difference in slopes between the two regimes) get small as the sample size increases, then the asymptotic distribution of the...