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It is important to understand to what extent, and in what perspectives, cyber attacks can be predicted. Despite its evident importance, this problem was not investigated until very recently, when we proposed using the innovative methodology of gray-box prediction. This methodology advocates the use of gray-box models, which accommodate the statistical properties/phenomena exhibited by the data. Specifically, we showed that gray-box models that accommodate the long-range dependence phenomenon can predict the attack rate (i.e., the number of attacks per unit time) 1-h ahead-of-time with an accuracy of 70.2%-82.1%. To the best of our knowledge, this is the first result showing the feasibility of prediction in this domain. We observe that the prediction errors are partly caused by the models' incapability in predicting the large attack rates, which are called extreme values in statistics. This motivates us to analyze …