Market Crashes and Time-Translation Invariance

Abstract

The general framework for quantitative technical analysis of market prices is revisited and extended. The concept of a global time-translation invariance and its spontaneous violation and restoration is introduced and discussed. We find that different temporal patterns leading to some famous crashes (e.g., bubbles, hockey sticks, etc.) exhibit analogous probabilistic distributions found only in the time series for the stock market indices. A number of examples of crashes are presented. We stress that our goal here is to study the crash as a particular phenomenon created by spontaneous time-translation symmetry breaking/restoration. We ask only “how to calculate and interpret the probabilistic pattern which we encounter in the day preceding crash, and how to calculate the typical market reactions to shock?”.

Keywords

• market crashes
• time-translation invariance
• replica symmetry violation
• exponential approximants
• Gompertz approximants
• logistic approximants