Although exchange rates appear to follow a random walk when tested aga
inst linear alternatives, the null hypothesis of a random walk is reje
cted against a cubic alternative which embodies the intuition that the
rate of mean-reversion increases with distance from equilibrium. A po
ssible theoretical foundation for such a model is suggested. The model
is tested on bilateral real exchange rates between four major currenc
ies, and on the real effective exchange rate of these four plus the Au
stralian dollar. The cubic model consistently outperforms its linear c
ounterpart and the results imply that real exchange rates are in fact
stationary.