Abstract
The assessment of time irreversibility, i.e., of the lack of invariance of the statistical properties of a system under the operation of time reversal, is a topic steadily gaining attention within the research community. Irreversible dynamics have been found in many real-world systems, with alterations being connected to, for instance, pathologies in the human brain, heart and gait, or to inefficiencies in financial markets. Assessing irreversibility in time series is not an easy task, due to its many aetiologies and to the different ways it manifests in data. It is thus not surprising that several numerical methods have been proposed in the last decades, based on different principles and with different applications in mind. In this contribution we review the most important algorithmic solutions that have been proposed to test the irreversibility of time series, their underlying hypotheses, computational and practical limitations, and their comparative performance. We further provide an open-source software library that includes all tests here considered. As a final point, we show that “one size does not fit all”, as tests yield complementary, and sometimes conflicting views to the problem; and discuss some future research avenues.
Highlights
We described the main tests designed to detect the irreversible nature of time series, and evaluated eight of them under different conditions, e.g., for different time series lengths or in the presence of noise and extreme values
There are essentially two approaches to time-reversal symmetry: one in which this is seen a geometric property of a process, typically a stochastic one
The other, in which time-reversal symmetry is related to fundamental physical properties underlying such a process
Summary
Time reversal symmetry is the symmetry of a physical law or a realisation of a physical phenomenon under the time-reversal transformation t 7→ −t
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