Solar energy is expected to provide a major contribution to the future global energy supply, while helping the transition toward a carbon-free economy. Because of its variable character, its efficient use will necessitate trustworthy forecast information of its availability in a variety of spatial and time scales, depending on application. This study proposes a new forecasting approach for irradiance time series that combines mutual information measures and an Extreme Learning Machine (ELM). The method is referred to as Minimum Redundancy - Maximum Relevance (MRMR). To assess the proposed approach, its performance is evaluated against four scenarios: long window (latest 50 variables), short window (latest 5 variables), standard Principal Components Analysis (PCA) and clear-sky model. All these scenarios are applied to three typical forecasting horizons (15-min ahead, 1-h ahead and 24-h ahead). Based on measured irradiance data from 20 sites representing a variety of climates, the test results reveal that the selection of a good set of relevant variables positively impacts the forecasting performance of global solar radiation. The present findings show that the proposed approach is able to improve the accuracy of solar irradiance forecasting compared to other proposed scenarios.