AbstractThe Purchasing Power Parity (PPP) hypothesis is one of the most important theoretical relationships in international economics. However, its empirical support remains controversial. We propose an alternative way of modelling the real exchange rate in five industrialized countries in relation to the US dollar, by means of fractionally integrated ARIMA models (i.e. ARFIMA). This approach allows us to capture the low‐frequency dynamics relevant for examination of the long‐run parity. A crucial fact when estimating with parametric approaches is that the model must be correctly specified, otherwise the estimates are likely to be inconsistent. In fact, misspecification of the short‐run components of the series can invalidate the estimation of its long‐run behaviour. We propose a model selection criterion based on LR tests on nested parametric hypotheses along with other several likelihood‐based criteria. As a validation method of the specified model, we suggest the use of Robinson's (1994) tests. Our empirical results indicate that the PPP might hold as a long‐run proposition. Copyright © 2002 John Wiley & Sons, Ltd.