A detailed parametric analysis is presented, where the recent method based on the reservoir computing paradigm, including its statistical robustness, is studied. It is observed that the prediction capabilities of the reservoir computing approach strongly depend on the random initialization of both the input and the reservoir layers. Special emphasis is put on finding the region in the hyperparameter space where the ensemble-averaged training and generalization errors together with their variance are minimized. The statistical analysis presented here is based on the projection on proper elements method.