With the increase in solar energy penetration in electric power systems, it is necessary to predict future solar radiation. With this, the solar power generation capacity can be predicted, allowing accurate scheduling for other sources. The solar radiation or the clearness index (CI) prediction was already presented using classical time series methods, artificial intelligence algorithms, among other approaches. In this paper, two methods are proposed to predict the CI. The first one solves a stochastic realization problem to find a mathematical model for the stochastic process that describes the CI. Then, a state observer is implemented to predict its future values. The second one performs the k-Nearest Neighbors (k-NN) regression algorithm for time series forecasting using two different approaches: the traditional k-NN and a recursive version proposed by the authors. As far as the authors know, the statistical and the recursive k-NN methods are different from the ones found in the literature to predict the CI. The methods were implemented and compared for short and long-term predictions. The results illustrate that one approach is more accurate than the other, depending on the prediction horizon. The comparison between the methods for different horizons is another contribution of this paper.