When the first terms of a sequence are known, a method which gives an approximation of the following ones is called a prediction method. Such methods have already been studied by Allan, Gilewicz, Kiwi, Levin, Prévost, Sidi, Trias, Vekemans, Weissmann, etc.

In this paper, we focus on the E-prediction which has been defined and studied by Brezinski and Redivo Zaglia.

The definition of a prediction method being quite weak, we also talk about consistency in order to appraise the specifications of the E-prediction. So, in exploiting a paper of Mortreux and Prévost dealing with acceleration properties of the E-algorithm, we prove some results of consistency.