The motivation for this paper was the introduction of novel short-term models to trade the FTSE 100 and DAX 30 exchange-traded funds (ETF) indices. There are major contributions in this paper which include the introduction of an input selection criterion when utilizing an expansive universe of inputs, a hybrid combination of partial swarm optimizer (PSO) with radial basis function (RBF) neural networks, the application of a PSO algorithm to a traditional autoregressive moving model (ARMA), the application of a PSO algorithm to a higher-order neural network and, finally, the introduction of a multi-objective algorithm to optimize statistical and trading performance when trading an index. All the machine learning-based methodologies and the conventional models are adapted and optimized to model the index. A PSO algorithm is used to optimize the weights in a traditional RBF neural network, in a higher-order neural network (HONN) and the AR and MA terms of an ARMA model. In terms of checking the statistical and empirical accuracy of the novel models, we benchmark them with a traditional HONN, with an ARMA, with a moving average convergence/divergence model (MACD) and with a naive strategy. More specifically, the trading and statistical performance of all models is investigated in a forecast simulation of the FTSE 100 and DAX 30 ETF time series over the period January 2004 to December 2015 using the last 3years for out-of-sample testing. Finally, the empirical and statistical results indicate that the PSO-RBF model outperforms all other examined models in terms of trading accuracy and profitability, even with mixed inputs and with only autoregressive inputs. Copyright (c) 2016 John Wiley & Sons, Ltd.