Uncertainty in Functional Network Representations of Brain Activity of Alcoholic Patients

Algorithmic Approaches for Assessing Irreversibility in Time Series: Review and Comparison

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.

Assessing time series irreversibility through micro-scale trends

Time irreversibility, defined as the lack of invariance of the statistical properties of a system or time series under the operation of time reversal, has received increasing attention during the last few decades, thanks to the information it provides about the mechanisms underlying the observed dynamics. Following the need of analyzing real-world time series, many irreversibility metrics and tests have been proposed, each one associated with different requirements in terms of, e.g., minimum time series length or computational cost. We here build upon previously proposed tests based on the concept of permutation patterns but deviating from them through the inclusion of information about the amplitude of the signal and how this evolves over time. We show, by means of synthetic time series, that the results yielded by this method are complementary to the ones obtained by using permutation patterns alone, thus suggesting that "one irreversibility metric does not fit all." We further apply the proposed metric to the analysis of two real-world data sets.