Integrating a large amount of wind energy into the bulk power grid has put forth great challenges for operations planning and system reliability. In particular, a complication that arises is that wind generation is highly variable (stochastic) and non-dispatchable, thus making it difficult to guarantee that the load and generation remain balanced at each instant. This uncertainty of wind generation impacts decision making at various system levels, and mischaracterizing the uncertainty can lead to spilt generation. In this work, the supply-side uncertainty is investigated by developing a realistic Markov chain model for wind generation forecasting. Specifically, using extensive measurement data obtained from an actual wind farm, a spatiotemporal analysis of the aggregate wind generation output from the farm is performed. One critical observation from empirical data is that the wind power output from the turbines are not necessarily equal even if they are identical and colocated. Using tools from graph theory and time-series analysis, a systematic procedure to characterize the statistical distribution of the aggregate wind power output from the farm is constructed. The procedure developed is amenable to the case when the farm has turbines from multiple classes, e.g., when they belong to multiple manufacturers or when they are deployed with different hub heights. The temporal dynamics of the aggregate wind power is characterized using auto-regression analysis, while taking into account the diurnal non-stationarity and the seasonality. Building on these spatial and temporal characterizations, a realistic, finite state Markov chain model for forecasting the aggregate wind power in a rigorous optimization framework is developed.