Stochastic local and moderate departures from a unit root and its application to unit root testing

Local-to-unity and moderate-deviations specifications have been popular alternatives to unit root modeling. This article considers another kind of departures from a root, the form c v t / T β , where is random determines distance root. We classify stochastic into two types: local moderate. classification task completed by investigating asymptotic behavior tests that assume (STUR) processes as alternative hypothesis. The local-to-unity model arises when = 3 4 ; in this case, test statistics limiting distributions different those under null, their powers are greater than size. Moderate deviations emerge 1 2 ≤ < which case diverge. also propose new for against an STUR, whose construction based on limit theory developed article. To evaluate performance these tests, we derive Gaussian power envelope approximate model.