Do real exchange rates really follow threshold autoregressive or exponential smooth transition autoregressive models?

Nonlinear models, especially threshold autoregressive [TAR] and exponential smooth transition autoregressive [ESTAR] classes, are widely applied for modeling real exchange rates in order to examine the validity of purchasing power parity [PPP]. Even though the nonlinear models are theoretically well-motivated, some of the recent findings cast doubts on their relevance for real exchange rates. In particular, the nonlinear models do not necessarily yield improved out-of-sample forecasts over linear models and add little value in resolving the well-documented PPP puzzle. Utilizing a nonparametric entropy measure of dependence proposed by Granger et al. (2004), we show, in this study, that the real exchange rates from four major countries had exhibited quite strong nonlinear serial dependence, which linear autoregressive models fail to replicate. Furthermore, the nonlinear TAR and ESTAR models estimated for the real exchange rates also have some difficulty in generating significant serial dependence structure actually observed in the data. Overall, other nonlinear models than the currently entertained TAR and ESTAR should be considered to study the dynamics of the real exchange rates.