This study examines time series from five European Stock Markets (UK. Germany, Belgium, Spain and Greece). Based on empirical evidence concerning nonlinear dependence, long-term memory effects and low-dimensional chaos, we assess the predictability of the series and determine the appropriate parameters for neural network modeling. We apply artificial neural network forecasting data sets from the semi-chaotic Greek Stock Exchange and utilize the outputs in the construction of a trading system. It is found that the neural network trading system performs significantly above random chance and other investment strategies.