School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Extreme Events and Emergency Scales

Document Type

Book Chapter

Publication Date

7-2021

Abstract

An event is extreme if its magnitude exceeds the threshold. A choice of a threshold is subject to uncertainty caused by a method, the size of available data, a hypothesis on statistics, etc. We assess the degree of uncertainty by the Shannon’s entropy calculated on the probability that the threshold changes at any given time. If the amount of data is not sufficient, an observer is in the state of Lewis Carroll’s Red Queen who said “When you say hill, I could show you hills, in comparison with which you’d call that a valley”. If we have enough data, the uncertainty curve peaks at two values clearly separating the magnitudes of events into three emergency scales: subcritical, critical, and extreme. Our approach to defining the emergency scale is validated by 39 years of Standard and Poors 500 (S&P500) historical data.

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© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG.

https://rdcu.be/dYAFQ

Publication Title

Mathematical Methods in Modern Complexity Science

DOI

https://doi.org/10.1007/978-3-030-79412-5_6

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