Eleven statistical and machine learning tools are analyzed and applied to hourly solar irradiation forecasting for time horizon from 1 to 6 hours. A methodology is presented to select the best and most reliable forecasting model according to the meteorological variability of the site. To make the conclusions more universal, solar data collected in three sites with low, medium and high meteorological variabilities are used: Ajaccio, Tilos and Odeillo. The datasets variability is evaluated using the mean absolute log return value. The models were compared in term of normalized root mean square error, mean absolute error and skill score. The most efficient models are selected for each variability and temporal horizon: for the weak variability, auto-regressive moving average and multi-layer perceptron are the most efficient, for a medium variability, auto-regressive moving average and bagged regression tree are the best predictors and for a high one, only more complex methods can be used efficiently, bagged regression tree and the random forest approach.

A global horizontal irradiation prediction (from 1 hour to 6 hours) is performed using 2 persistence models (simple and "smart" ones) and 4 machine learning tools belonging to the regression trees methods family (normal, pruned, boosted and bagged). A prediction band is associated to each forecast using methodologies based on: bootstrap sampling and k-fold approach, mutual information, stationary time series process with clear sky model, quantiles estimation and cumulative distribution function. New reliability indexes (gamma index and gamma test) are built from the mean interval length (MIL) and prediction interval coverage probability (PCIP). With such methods and error metrics, good prediction bands are estimated for Ajaccio (France) with a MIL close to 113 Wh/m², a PCIP reaching 70% and a gamma index lower than 0.9.

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