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Wind power presented a remarkable growth in the first decade of the 21st century, highly sustained by the economical and ecological benefits of this technology. Not only has it significantly contributed to reduce the dependence on fossil fuels in the production of electrical energy, wind power has also allowed to save great amounts of greenhouse gases emissions. This growth leads to an inevitable also increasing impact of the wind energy electrical energy produced making use of the wind resource in the electrical system, which raises issues like network stability and the assurance of the supply to all loads connected to the electrical grid. An accurate forecast of the available wind energy for the forthcoming hours helps to perform a good planning and scheduling of the network, which minimizes the risks of this impact. Also, with the liberalization of the electrical markets worldwide, the wind power forecasting reveals itself important in order for the developers to estimate the correct bids to place in the respective market. This work addresses the issue of forecasting wind with two statistical models, the Autoregressive Moving Average and Artificial Neural Networks, making use of historical wind speed data. The basics of forecasting with these models are presented, and their forecasting performance is compared in two different case studies. Similar criteria are defined in order to adjust the required settings in both models. Finally, conclusions are drawn about the performance and the results obtained, considering the available data and the differences between the inherent characteristics to both models.