Optimal integration of wind energy into power systems calls for high quality wind power predictions. State-of-the-art forecasting systems typically provide forecasts for every location individually, without taking into account information coming from the neighbouring territories. It is however intuitively expected that owing to the inertia in meteorological systems such local approach to power forecasting is sub-optimal. Indeed, errors in meteorological forecasts might translate to fronts of imbalances, i.e. taking the form of a band of forecast errors propagating across entire regions. My research work deals with the proposal and evaluation of new mathematical models and forecasting methods for short-term wind power forecasting, accounting for space-time dynamics based on geographically distributed information. Different forms of power predictions are considered, starting from traditional point forecasts, then extending to marginal predictive densities and, finally, considering multivariate space-time trajectories. Point predictions is the most classical approach to wind power forecasting, only providing single-valued estimates of the expected future power generation. The objective is to introduce a statistical model which would improve the quality of state-of-the-art prediction methods by accounting for the fact that forecasts errors made by such locally-optimized forecasting methods propagate in space and in time under the influence of prevailing weather conditions. Subsequently, the extension from point to probabilistic forecasts is dealt with, hence requiring to describe the uncertainty associated with the point predictions previously generated. Both parametric and non-parametric approaches to forming predictive densities are considered, while ways to include space-time effects into the corresponding models are analysed. As a final step, emphasis is placed on generating space-time trajectories: this calls for the prediction of joint multivariate predictive densities describing wind power generation at a number of distributed locations and for a number of successive lead times. In addition to new improved approaches to wind power forecasting, a part of the research is devoted to problems related to the assessment of high-dimensional (multivariate) probabilistic forecasts.