Artificial neural networks (ANNs) with the logistic transforms are popular methods to increase the accuracy of performance forecasting due to their functional flexibility. In this paper, we estimate the accuracy of the ANNs models by conducting a data-driven search for optimal specifications. Our tests on foreign exchange rate forecast for the Korean won/US dollar show that the ANNs are superior to linear models. The superiority of the ANNs, however, does not hold for the Japanese yen/US dollar exchange rates. We use the success ratio (SR) as the out-of-sample forecasting performance evaluation. The directional accuracy (DA) test and the forecast comparison statistics of Diebold and Mariano (DM) are applied to assess the relative forecast performance of the ANNs as well. For the Korean won spot rate, it seems that there is much to be gained by using the ANNs for predicting the direction of change. The DA test results also show that the SR from the ANNs is generally greater than that from the AR models. For the Japanese yen, the ANNs achieve a lower SR in most cases. The balance between the in-sample fit and the out-of-sample forecast performance is well achieved for the Korean won exchange rate, but not for the Japanese yen exchange rate. This study is significant in that no previous works that evaluated the accuracy of exchange rate forecasts have applied a variety of tests in order to ascertain whether the ANNs of out-of-sample forecast performance actually achieve directional accuracy as economic criteria.