Two competitive models and their identification problem: The ESTAR and TSTAR model

Determining good parameter estimates in ESTAR models is known to be diffcult. We show that the phenomena of getting strongly biased estimators is a consequence of the so-called identifcation problem, the problem of properly distinguishing the transition function in relation to extreme parameter combinations. This happens in particular for either very small or very large values of the error term variance. Furthermore, we introduce a new alternative model -the TSTAR model- which has similar properties as the ESTAR model but reduces the effects of the identifcation problem. We also derive a linearity and a unit root test for this model.