Testing for a Unit Root in the Asymmetric Nonlinear Smooth Transition Framework

This paper proposes a simple testing procedure to detect the presence of nonlinear but global stationary logistic smooth transition autoregressive processes. This testing procedure nests the one developed by Kapetanios et al. (2003) that accommodates specifically the alternative of a global stationary ESTAR process. The present work makes a threefold contribution to the literature. First, it derives the limiting nonstandard distribution of the proposed test. Second, the paper finds via Monte Carlo simulations that under the alternative of a globally stationary LSTAR process, this new test has better power than a standard Dickey-Fuller test. Third, an empirical application of the test to real exchange data in OECD countries rejects the null of a unit root more often than a simple Dickey-Fuller. This finding provides more evidence in favor of nonlinear PPP mean-reversion.