This chapter presents a method that combines the spatial model feature and time series model feature in a method known as the Gaussian spatio-temporal autoregressive model. Assuming separability suggests the lack of interaction between the spatial and temporal components and implies full symmetry in the spatio-temporal covariance structure, which brings up the concept of spatio-temporal symmetry. The physical differences between local wind fields and large-scale atmospheric processes require special adjustments to the spatio-temporal resolution used to analyze wind measurements, in order to reveal the underlying asymmetry pattern. The spatio-temporal dynamics within a wind farm are affected by the wake effect because the rotating turbine blades cause changes in the speed, direction and turbulence intensity of the propagating wind. The short-term wind forecasting may benefit from using an asymmetric, separable spatio-temporal covariance structure. A spatio-temporal model can be used together with some machine learning models to improve further the forecasting capability.