The objective of this paper is to investigate the persistence in Turkish real exchange rates (RER) using unit root tests and autoregressive fractionally integrated moving average (ARFIMA) models. We consider two RERs, one in terms of the German DM and the other in terms of the US$. ne plots of these RERs (based on both wholesale price indices and consumer price indices)for the period 1984.01-2000.09 reveal that they contain multiple shifts in their deterministic terms, one of which may need to be treated as an outlier for some of the series. Hence, when this aspect is taken into account in both the unit root tests and the ARFIMA models, we find strong evidence of stationarity in almost all series, together with significant long-memory components. These findings, then, support the validity of the absolute version of the "quasi" purchasing power parity hypothesis for Turkey.