In recent years, an important increase in the amount and impact of Distributed Denial of Service (DDoS) threats has been reported by the different information security organizations. They typically target the depletion of the computational resources of the victims, hence drastically harming their operational capabilities. Inspired by these methods, Economic Denial of Sustainability (EDoS) attacks pose a similar motivation, but adapted to Cloud computing environments, where the denial is achieved by damaging the economy of both suppliers and customers. Therefore, the most common EDoS approach is making the offered services unsustainable by exploiting their auto-scaling algorithms. In order to contribute to their mitigation, this paper introduces a novel EDoS detection method based on the study of entropy variations related with metrics taken into account when deciding auto-scaling actuations. Through the prediction and definition of adaptive thresholds, unexpected behaviors capable of fraudulently demand new resource hiring are distinguished. With the purpose of demonstrate the effectiveness of the proposal, an experimental scenario adapted to the singularities of the EDoS threats and the assumptions driven by their original definition is described in depth. The preliminary results proved high accuracy.