Time-reversal asymmetry in financial systems

TL;DR

This paper analyzes large-fluctuation dynamics in Chinese and German financial markets, revealing time-reversal symmetry at minute scales and asymmetry at daily scales, mainly driven by external forces causing non-stationarity.

Contribution

It uncovers the scale-dependent time-reversal symmetry properties and identifies external forces as the main cause of asymmetry and non-stationarity in financial fluctuations.

Findings

Power-law relaxation before and after large fluctuations

Time-reversal symmetry at minute scale, asymmetry at daily scale

External forces induce asymmetry and non-stationarity

Abstract

We investigate the large-fluctuation dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after the large fluctuations is characterized by a power law, and the exponents $p_\pm$ usually vary with the strength of the large fluctuations. The large-fluctuation dynamics is time-reversal symmetric at the time scale in minutes, while asymmetric at the daily time scale. Careful analysis reveals that the time-reversal asymmetry is mainly induced by external forces. It is also the external forces which drive the financial system to a non-stationary state. Different characteristics of the Chinese and German stock markets are uncovered.