In this paper, we study an evolutionary framework for the optimization of various types of neural network structures and parameters. Three different evolutionary algorithms – the genetic algorithm (GA), differential evolution (DE) and the particle swarm optimizer (PSO) – are developed to optimize the structure and the parameters of three different types of neural network: multilayer perceptrons (MLPs), recurrent neural networks (RNNs) and radial basis function (RBF) neural networks. The motivation of this project is to present novel methodologies for the task of forecasting and trading financial indexes. More specifically, the trading and statistical performance of all models is investigated in a forecast simulation of the SPY and the QQQ exchange-traded funds (ETFs) time series over the period January 2006 to December 2015, using the last three years as out-of-sample testing. As it turns out, the RBF-PSO, RBF-DE and RBF-GA ensemble methodologies do remarkably well and outperform all of the other models.