TY - JOUR
T1 - Extreme events and emergency scales
AU - Smirnov, Veniamin
AU - Ma, Zhuanzhuan
AU - Volchenkov, Dimitri
N1 - Funding Information:
Work done under contract with the AVX Aircraft Company Contract #W911W6-13-2-0004.
Funding Information:
VS acknowledges the support of Department of Mathematics and Statistics of Texas Tech University provided him a temporary Research Assitant position. We are grateful to Dr. M. Toda for her support. Work was done under a contract #W911W6-13-2-0004 with the AVX Aircraft Company.
Publisher Copyright:
© 2020
PY - 2020/11
Y1 - 2020/11
N2 - 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 Poor's 500 (S&P500) historical data.
AB - 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 Poor's 500 (S&P500) historical data.
KW - Emergency scales
KW - Extreme events
KW - Uncertainty of threshold
UR - http://www.scopus.com/inward/record.url?scp=85085638607&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2020.105350
DO - 10.1016/j.cnsns.2020.105350
M3 - Review article
AN - SCOPUS:85085638607
SN - 1007-5704
VL - 90
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
M1 - 105350
ER -