Short-term wind farm power forecasting is studied by exploiting the spatio-temporal correlation between individual turbine's power output. A multivariate time series model for wind farm power generation is developed by using vector autoregression (VAR). In order to avoid the possible over-fitting issues caused by a large number of autoregressive coefficients and the impact on the forecasting performance of VAR models, a sparsified autoregressive coefficient matrix is constructed by utilizing the information on wind direction, wind speed and wind farm's layout. Then, the VAR model parameters are obtained through maximum likelihood estimation of real-time measurement data, by taking into account the sparse structure of the autoregressive coefficient matrix. The proposed approach is compared with univariate autoregressive models through numerical experiments, resulting in significant improvement, which is attributed to the turbine-level correlation captured by the developed VAR model.