The process followed by PPP data. On the properties of linearity tests

Recent research has reported the lack of correct size in stationarity test for PPP deviations within a linear framework. However, theoretically well motivated non-linear models, such as the ESTAR, appear to parsimoniously fit the PPP data and provide an explanation for the PPP 'puzzle'. Employing Monte Carlo experiments the size and power of the non-linear tests are analysed against a variety of nonstationary hypotheses. Aslo the ESTAR model is fitted to data from high inflation economies. The results provide further support for ESTAR specification.