Signatures of extreme events in the cumulative entropic spectrum

Abstract: In this study, the cumulative effect of the empirical probability distribution of a random variable is identified as a factor that amplifies the occurrence of extreme events in datasets. To quantify this observation, a corresponding information measure is introduced, drawing upon Shannon entropy for joint probabilities. The proposed approach is validated using selected market data as case studies, encompassing various instances of extreme events. In particular, the results indicate that the introduced cumulative measure exhibits distinctive signatures of such events, even when the data is relatively noisy. These findings highlight the potential of the discussed concept for developing a new class of related indicators or classifiers.