In this paper, we propose a spatio-temporal analysis approach for short-term forecasting of wind farm generation. Specifically, using extensive measurement data from an actual wind farm, the probability distribution and the level crossing rate (LCR) of wind farm generation are characterized by using tools from graphical learning and time-series analysis. Based on these spatial and temporal characterizations, finite state Markov chain models for wind farm generation are developed. Point-forecast of wind farm generation is derived using the Markov chains and integrated into power system economic dispatch. Numerical study on economic dispatch using the IEEE 30-bus test system demonstrates the significant improvement compared with conventional wind-speed-based forecasting methods.