Only one thousand stations around the world measures solar radiation sometimes with a poor quality. The objective of this paper is to show if solar irradiations at short time scale, hourly and 5-min, (very under-studied time-step) can be estimated from more available and cheaper data using Artificial Neural Networks. 7 meteorological and 3 calculated parameters are used as inputs; 1023 inputs combinations are possible for each time-step; the best inputs combinations are pursued. A variable selection method based on Pearson's coefficient is firstly used between inputs and between output and inputs; some inputs are redundant (particularly calculated ones) and/or with a weak link with solar radiation (as wind speed and direction), sunshine duration is strongly correlated with solar irradiation. The models have a good adequacy mainly with sunshine duration in the input set. For hourly data, the performances of the 6 and 10 inputs model are nRMSE = 13.90% (nMAE = 13.28%, R-2 = 0.979) and nRMSE = 13.33% (nMAE = 12.72%, R-2 = 0.9812); without sunshine duration, the model nRMSE (with 5 inputs) falls to 28.27%. For 5-min data, the 6 and 10 inputs models have a nRMSE equal to 19.35% and 18.65% which is very good for such a time-step. A comparison with literature highlighted the quality of these models. (C) 2016 Elsevier Ltd. All rights reserved.