We examine directional predictability in foreign exchange markets using a model-free statistical evaluation procedure. Based on a sample of foreign exchange spot rates and futures prices in six major currencies, we document strong evidence that the directions of foreign exchange returns are predictable not only by the past history of foreign exchange returns, but also the past history of interest rate differentials, suggesting that the latter can be a useful predictor of the directions of future foreign exchange rates. This evidence becomes stronger when the direction of larger changes is considered. We further document that despite the weak conditional mean dynamics of foreign exchange returns, directional predictability can be explained by strong dependence derived from higher-order conditional moments such as the volatility, skewness and kurtosis of past foreign exchange returns. Moreover, the conditional mean dynamics of interest rate differentials contributes significantly to directional predictability. We also examine the co-movements between two foreign exchange rates, particularly the co-movements of joint large changes. There exists strong evidence that the directions of joint changes are predictable using past foreign exchange returns and interest rate differentials. Furthermore, both individual currency returns and interest rate differentials are also useful in predicting the directions of joint changes. Several sources can explain this directional predictability of joint changes, including the level and volatility of underlying currency returns.