The increasing sophistication of wind turbine design and control generates a need for high-quality wind data. The relatively limited set of available measured wind data may be extended with computer generated data, for example, to make reliable statistical studies of energy production and mechanical loads. Here, a data-driven model for the generation of surrogate wind speeds is compared with two state-of-the-art time series models that can capture the probability distribution and the autocorrelation of the target wind data. The proposed model, based on the phase-randomised Fourier transform, can generate wind speed time series that possess the power spectral density of the target data and converge to their generally non-Gaussian probability distribution with an arbitrary, user-defined precision. The model performance is benchmarked in terms of probability distribution, power spectral density, autocorrelation, and nonstationarities such as the diurnal and seasonal variations of the target data. Comparisons show that the proposed model can outperform the selected models in reproducing the statistical descriptors of the input datasets and is able to capture the nonstationary diurnal and seasonal variations of the wind speed.