A medium term stochastic load model using the hourly AMI load data aggregated at transformers and feeders is introduced. Load model frequency domain statistical parameters are derived from spectral analysis of AMI data. The load model is driven by a weather index based on Heating-Cooling Day Degree. This index is incorporated into the model using local, hourly weather data. Advantages of the proposed load model are discussed. Performance comparisons between the proposed model and several time-domain methods are presented.