Baillie and Bollerslev (1989) have recently argued that nominal dollar spot exchange rates are cointegrated. Here we examine an immediate implication of their finding, namely, that cointegration implies an error-correction representation yielding forecasts superior to those from a martingale benchmark, in light of a large earlier literature highlighting the predictive superiority of the martingale. In an out-of-sample forecasting exercise, we find the martingale model to be superior. We then perform a battery of improved cointegration tests and find that the evidence for cointegration is much less strong than previously thought, a result consistent with the outcome of the forecasting exercise.