We propose a stylized exchange rate model based on diversity and weight ofopinion. Our model departs from standard assumptions in that we allow forheterogeneous agents. We show that such a model can explain both the observedvolatility and the persistence of real and nominal exchange rate movements and thusin some measure resolves Rogoffs (1996) purchasing power parity puzzle. Ourempirical analysis reconciles the well-known difficulties in beating the random walkforecast model with the statistical evidence of nonlinear mean reversion in deviationsfrom fundamentals. We find strong evidence of long-horizon predictability both intheory and in practice. We also explain why it is difficult to exploit this predictabilityin out-of-sample forecasts. Our results not only lend support to economists' beliefsthat the exchange rate is inherently predictable, but they also help us to understandthe reluctance of applied forecasters to abandon chartists methods in favor ofmodels based on economic fundamentals.