Corbae and Ouliaris (1991) examined Australia's long-nm real exchange rate and concluded that because the data follow a random walk, purchasing power parity does not hold as a long-run equilibrium relation. We re-examine their data by calculating non-parametric measures of persistence and estimating functionally integrated ARMA models. We find that shocks to the real exchange rate have a finite life. This result is consistent with long-run purchasing power parity.