Extreme events and emergency scales.

Area of Science:

• Financial risk analysis
• Statistical modeling
• Time series analysis

Background:

• Extreme events are defined by exceeding a threshold, but threshold selection involves uncertainty.
• Insufficient data leads to ambiguity in event magnitude classification, akin to the Red Queen's observation.

Purpose of the Study:

• To develop a method for quantifying uncertainty in extreme event threshold selection.
• To establish a robust framework for defining emergency scales based on data availability and statistical properties.

Main Methods:

• Utilizing Shannon's entropy to measure the probability of threshold changes over time.
• Analyzing the uncertainty curve to identify critical points for scale separation.
• Validating the approach with 39 years of Standard and Poor's 500 (S&P500) historical data.

Main Results:

• The uncertainty quantification method effectively identifies thresholds.
• Sufficient data allows the uncertainty curve to peak, clearly separating event magnitudes.
• Three distinct emergency scales (subcritical, critical, extreme) are defined.

Conclusions:

• Shannon's entropy provides a reliable measure for assessing uncertainty in extreme event thresholds.
• The proposed method enables objective classification of events into emergency scales.
• The validated approach offers a valuable tool for financial risk management and event analysis.