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Accurate wind speed forecasting is a fundamental requirement for advanced and economically viable large-scale wind power integration. The hybridization of the quaternion-valued neural networks and stationary wavelet transform has not been proposed before. In this paper, we propose a novel wind-speed forecasting model that combines the stationary wavelet transform with quaternion-valued neural networks. The proposed model represents wavelet subbands in quaternion vectors, which avoid separating the naturally correlated subbands. The model consists of three main steps. First, the wind speed signal is decomposed using the stationary wavelet transform into sublevels. Second, a quaternion-valued neural network is used to forecast wind speed components in the stationary wavelet domain. Finally, the inverse stationary wavelet transform is applied to estimate the predicted wind speed. In addition, a softplus quaternion variant of the RMSProp learning algorithm is developed and used to improve the performance and convergence speed of the proposed model. The proposed model is tested on wind speed data collected from different sites in China and the United States, and the results demonstrate that it consistently outperforms similar models. In the meteorological terminal aviation routine (METAR) dataset experiment, the proposed wind speed forecasting model reduces the mean absolute error, and root mean squared error of predicted wind speed values by 26.5% and 33%, respectively, in comparison to several existing approaches.