In this paper, we show that neural networks can be used to uncover the non-linearity that exists in the financial data. First, we follow a traditional approach by analysing the deterministic/stochastic characteristics of the Portuguese stock market data and some typical features are studied, like the Hurst exponents, among others. We also simulate a BDS test to investigate nonlinearities and the results are as expected: the financial time series do not exhibit linear dependence. Secondly, we trained four types of neural networks for the stock markets and used the models to make forecasts. The artificial neural networks were obtained using a three-layer feed-forward topology and the back-propagation learning algorithm. The quite large number of parameters that must be selected to develop a neural network forecasting model involves some trial and as a consequence the error is not small enough. In order to improve this we use a nonlinear optimization algorithm to minimize the error. Finally, the output of the 4 models is quite similar, leading to a qualitative forecast that we compare with the results of the application of k-nearest-neighbor for the same time series

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• Physical Sciences - Natural Sciences