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The motivation for this paper is to investigate the use of alternative novel neural network architectures when applied to the task of forecasting and trading the ASE 20 Greek Index using only autoregressive terms as inputs. This is done by benchmarking the forecasting performance of 4 different neural network training algorithms with some traditional techniques, either statistical such as an autoregressive moving average model (ARMA), or technical such as a moving average convergence/divergence model (MACD), plus a naïve strategy. For the best training algorithm found, we used a genetic algorithm to find the best feature set, in order to enhance the performance of our models. More specifically, the trading performance of all models is investigated in a forecast and trading simulation on ASE 20 fixing time series over the period 2001-2009 using the last one and half year for out-of-sample testing. As it turns out, the combination of the neural network with genetic algorithm, does remarkably well and outperforms all other models in a simple trading simulation exercise and when more sophisticated trading strategies as transaction costs were applied.