The paper presents a systematic method to build dynamic stochastic models from wind speed measurement data. The resulting models fit any probability distribution and any autocorrelation that can be approximated through a weighted sum of decaying exponential and/or damped sinusoidal functions. The proposed method is tested by means of real-world wind speed measurement data with sampling rates ranging from seconds to hours. The statistical properties of the wind speed time series and the synthetic stochastic processes generated with the Stochastic Differential Equation (SDE)-based models are compared. Results indicate that the proposed method is simple to implement, robust and can accurately capture simultaneously the autocorrelation and probability distribution of wind speed measurement data. (C) 2019 Elsevier Ltd. All rights reserved.