The main purpose of this paper it is to show that machine learning methods (neural networks and k-nearest neighbours) can be used to uncover the non-linearity that exists in financial time series and provide high quality forecast. First, we analyse the linearity (BDS test) and stationarity (ADF, PP unit rot test) of the Portuguese stock market index, PSI20, and also some typical features are studied (descriptive statistics, Hurst exponents, among others). The first forecast it is provided by traditional linear ARMA models. Secondly, we train several types of neural networks for the PSI20 index and use the models to make 1 and 5-day forecasts. The artificial neural networks are obtained by using a three-layer feed-forward topology and the back-propagation learning algorithm. Thirdly, k-nearest neighbours chartist method it is used. Finally, we compare the out-of-sample forecast error (MAE) for the several models, in order to conclude about the forecasting performance.

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Time-series,ARMA,Artificial Neural Network,Forecasting