Effective and accurate forecasting of solar radiation plays a critically important role in the design of grid connected photovoltaic installations. However, this is an extremely challenging task because of inconsistencies in variable selection and the prohibitively expensive computational cost as the number of variables increases. Although the support vector machine (SVM) can be applied to forecast solar radiation, it includes a large number of redundant variables. With the intent of establishing an interpretable model, a penalized SVM has been proposed. However, these penalized approaches shrink the estimate, which results in inaccurate results. In order to overcome these drawbacks and improve the accuracy of forecasting, this study develops a novel approach referred to as "forward regression on the quadratic kernel support vector machine" (QKSVM-FR) for building a quadratic regression model using forward regression to select the important variables for forecasting the global horizontal radiation in the Tibet Autonomous Region. A fast and simple-to-implement computational algorithm is derived to perform the variable selection and forecasting tasks simultaneously. Furthermore, the SVM information criterion is utilized to select the kernel parameter to guarantee model consistency. The results of experiments directly confirm the outstanding forecasting performance of the proposed QKSVM-FR method compared to other existing methods. (C) 2017 Elsevier Ltd. All rights reserved.