Preprint Article Version 1 This version is not peer-reviewed

Assessing Time Series Reversibility through Permutation Patterns

Version 1 : Received: 3 August 2018 / Approved: 4 August 2018 / Online: 4 August 2018 (11:16:26 CEST)

A peer-reviewed article of this Preprint also exists.

Zanin, M.; Rodríguez-González, A.; Ruiz, E.M.; Papo, D. Assessing Time Series Reversibility through Permutation Patterns. Entropy 2018, 20, 665. Zanin, M.; Rodríguez-González, A.; Ruiz, E.M.; Papo, D. Assessing Time Series Reversibility through Permutation Patterns. Entropy 2018, 20, 665.

Journal reference: Entropy 2018, 20, 665
DOI: 10.3390/e20090665

Abstract

Time irreversibility, i.e. the lack of invariance of the statistical properties of a system under time reversal, is a fundamental property of all systems operating out of equilibrium. Time reversal symmetry is associated with important statistical and physical properties and is related to the predictability of the system generating the time series. Over the past fifteen years, various methods to quantify time irreversibility in time series have been proposed, but these can be computationally expensive. Here we propose a new method, based on permutation entropy, which is essentially parameter-free, temporally local, yields straightforward statistical tests, and has fast convergence properties. We apply this method to the study of financial time series, showing that stocks and indices present a rich irreversibility dynamics. We illustrate the comparative methodological advantages of our method with respect to a recently proposed method based on visibility graphs, and discuss the implications of our results for financial data analysis and interpretation.

Subject Areas

time irreversibility; permutation entropy; visibility graphs; efficient market hypothesis

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