fINANCIAL TIME SERIES—and foreign exchange rate forecasts in particular—are difficult to model [39J. Hsieh 115] and others [7| have demonstrated that foreign exchange and other financial time series follow a random walk and should therefore not be predictable much past 50 percent (the average performance of random walk models for foreign exchange markets). Neural networks provide a valuable tool for building nonlinear models of data, especially when the underlying laws governing the system are unknown [39]. Neural network forecasting models have outperformed