Abstract Markov chains (MCs) are statistical models used in many applications to model wind speed. Their main feature is the ability to represent both the statistical and temporal characteristics of the modelled wind speed data. However, MCs\ are not able to capture wind characteristics at high frequencies, and, by definition, in an MC\ the dependence on events far in the past is lost. This is reflected by a poor match of autocorrelation function of recorded data and artificially generated time series. This study presents a new method for generating artificial wind speed time series. This method is based on nested Markov chains (NMCs), which are an extension of MC\ models, where each state in the state space can be seen as a self-contained MC. The approach is designed to be flexible, so that the number and distribution of NMC\ states can be adjusted according to user requirements for model accuracy and computational efficiency. The model is tested on two datasets recorded in two UK\ locations, one onshore and one offshore. Results indicate that NMCs\ are able to capture the temporal self-dependence of wind speed data better than MCs, as shown by the better match of the autocorrelation functions of recorded and artificially generated time series.