A data-driven evaluation of thousands of statistics finds several families effective at distinguishing time-irreversibility but shows no single statistic works across all systems.
Zumbach, Time reversal invariance in finance, Quantitative Finance 9, 505 (2009)
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Identifying statistical indicators of temporal asymmetry using a data-driven approach
A data-driven evaluation of thousands of statistics finds several families effective at distinguishing time-irreversibility but shows no single statistic works across all systems.