The increasing sophistication of wind turbine design and control generates a need for high-quality data. Therefore, the relatively limited set of measured wind data may be extended with computer-generated surrogate data, e.g. to make reliable statistical studies of energy production and mechanical loads. This paper presents a data-driven, statistical model for the generation of realistic surrogate time series that is based on the phase-randomised Fourier transform. The proposed model simulates an ergodic, pseudo-random process that makes use of an iterative rank-reordering procedure to yield synthetic time series that possess the power spectral density of the target data and concurrently converges to the probability distribution of the target data with an arbitrary, user-defined precision. A comparison with two established data-driven modelling techniques for generating surrogate wind speeds is presented. The proposed model is tested under the same input conditions given in the test cases of the selected models, and its performance is investigated in terms of the agreement with the target statistical descriptors. Simulation results show that the proposed model can reproduce with high fidelity the statistical descriptors of the input datasets and is able to capture the nonstationary diurnal and seasonal variations of the wind speed.