Nonlinear mean-reversion to purchasing power parity: exponential smooth transition autoregressive models and stochastic unit root processes

Nonlinear exponential smooth transition autoregressive (ESTAR) models are recently very popular in modelling the deviation from purchasing power parity. This article, shows that there is a close relation between the ESTAR models estimated in Taylor et al. (2001) and stochastic unit root (STUR) processes of Granger and Swanson (1997) and McCabe and Tremayne (1995). Also, for a post-Bretton Woods sample period, the real exchange rates from four major countries are tested if they are better described as I(1), ESTAR or STUR processes.