Accurate prediction of solar radiation is of high importance for proper operation of the electrical grid. Over short horizons, forecasting solar irradiance is often performed by extrapolation of field measurements. Four tailored statistical models for forecasting hourly average solar irradiance are proposed and assessed in this paper. These follow from the well-known regression and ARIMA class of models, but bring into the model formulation various physically motivated additional features. These capture the distribution of solar radiation more effectively. Their performance is compared with the performance of a standard model used in the strictly black-box style often encountered in practice. Overall results demonstrate that the proposed models are significantly more accurate than the standard model, under conditions of mostly cloudy skies. (C) 2014 Elsevier Ltd. All rights reserved.