This paper uses monthly data on euro exchange rates vis-à-vis major currencies, covering the period 1999-2012, to compare the forecasting ability of alternative stochastic exchange rate representations. In particular, we test the out-of-sample forecasting performance of a random walk, a non-linear Markov switching regimes process, and a vector autoregressive representation reflecting the dynamics of linear structural exchange rate models. These statistical models are evaluated in terms of the root mean square error of one-month to twelve-month out-of-sample forecasts. The empirical evidence points to the random walk puzzle, that is, the superiority of the naïve model in forecasting exchange rates before the crisis of 2008. However, this outcome is consistently reversed following the 2008 financial turmoil and the naïve model seems to regain some of its forecasting power only after 2011. These results suggest that different stochastic representations are appropriate for the exchange rate depending on the presence of financial calmness or turbulence.