Exchange rate series generally follow nonlinear time paths. To be more precise, a typical exchange rate time series would be meandering. Meandering series are interesting, for they tend to be non-stationary in the short run yet mean reverting in the long run. This interesting time series characteristic, though, is surely one of the biggest difficulties that should be dealt with by the students of exchange rates. When we look back the decades-long attempts of modeling exchange rates, the Fama equation, a linear specification based on the uncovered interest parity (UIP) idea, seems to have been the workhorse model of exchange rate determination studies. The linear specification of the Fama equation might be an important drag when the meandering nature of the exchange rates are considered.