Identification problems in ESTAR models and a new model

In ESTAR models it is usually difficult to determine parameter estimates, as it can be observed in the literature. We show that the phenomena of getting strongly biased estimators is a consequence of the so-called identification 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 T-STAR model - which has similar properties as the ESTAR model but reduces the effects of the identification problem. We also derive a linearity and a unit root test for this model.