Unit root test against ESTAR with deterministic components

This article intends to notify that asymptotic distributions of the nonlinear unit root test statistics must be rigorously treated if deterministic components are included in the estimated regression. The simple inductive argument of replacing the standard Brownian motion by either the demeaned or demeaned and detrended ones usually adopted in the literature is invalid. New results on the asymptotic distributions of the t-ratio to test the null of the unit root against the nonlinear exponential smooth transition autoregressive (ESTAR) with deterministic components are provided.