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Wind energy is becoming a top contributor to the renewable energy mix, which raises potential reliability issues for the grid due to the fluctuating and intermittent nature of its source. This paper explores the use of Markov chain models for the analysis of wind power time-series. The proposed Markov chain model is based on a 2yr dataset collected from a wind turbine located in Portugal. The wind speed, direction and power variables are used to define the states and the transition matrix is determined using a maximum likelihood estimator based on multi-step transition data. The Markov chain model is analyzed by comparing the theoretically derived properties with their empirically determined analogues. Results show that the proposed model is capable of describing the observed statistics, such as wind speed and power probability density as well as the persistence statistics. It is demonstrated how the application of the Markov chain model can be used for the short-term prediction of wind power.