Considering that wind power is proportional to the cube of the wind speed variable, which is highly random, complex power grid management tasks have arisen as a result. Wind speed prediction in the short term is crucial for load dispatch planning and load increment/decrement decisions. The chaotic intermittency of speed is often characterised by inherent linear and nonlinear patterns, as well as nonstationary behaviour; thus, it is generally difficult to predict it accurately and efficiently using a single linear or nonlinear model. In this study, wavelet transform (WT), autoregressive integrated moving average (ARIMA), extreme gradient boosting trees (XGBoost), and support vector regression (SVR) are combined to predict high-resolution short-term wind speeds obtained from three Southern African Universities Radiometric Network (SAURAN) stations: Richtersveld (RVD); Central University of Technology (CUT); and University of Pretoria (UPR). This hybrid model is termed WT-ARIMA-XGBoost-SVR. In the proposed hybrid, the ARIMA component is employed to capture linearity, while XGBoost captures nonlinearity using the wavelet decomposed subseries from the residuals as input features. Finally, the SVR model reconciles linear and nonlinear predictions. We evaluated the WT-ARIMA-XGBoost-SVR’s efficacy against ARIMA and two other hybrid models that substitute XGBoost with a light gradient boosting machine (LGB) component to form a WT-ARIMA-LGB-SVR hybrid model and a stochastic gradient boosting machine (SGB) to form a WT-ARIMA-SGB-SVR hybrid model. Based on mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), coefficient of determination (R2), and prediction interval normalised average width (PINAW), the proposed hybrid model provided more accurate and reliable predictions with less uncertainty for all three datasets. This study is critical for improving wind speed prediction reliability to ensure the development of effective wind power management strategies.