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An improvement of the measurement of time series irreversibility with visibility graph approach

Zhenyu Wu, Pengjian Shang and Hui Xiong

Physica A: Statistical Mechanics and its Applications, 2018, vol. 502, issue C, 370-378

Abstract: We propose a method to improve the measure of real-valued time series irreversibility which contains two tools: the directed horizontal visibility graph and the Kullback–Leibler divergence. The degree of time irreversibility is estimated by the Kullback–Leibler divergence between the in and out degree distributions presented in the associated visibility graph. In our work, we reframe the in and out degree distributions by encoding them with different embedded dimensions used in calculating permutation entropy(PE). With this improved method, we can not only estimate time series irreversibility efficiently, but also detect time series irreversibility from multiple dimensions. We verify the validity of our method and then estimate the amount of time irreversibility of series generated by chaotic maps as well as global stock markets over the period 2005–2015. The result shows that the amount of time irreversibility reaches the peak with embedded dimension d=3 under circumstances of experiment and financial markets.

Keywords: Time series irreversibility; Visibility graph; Kullback–Leibler divergence (search for similar items in EconPapers)
Date: 2018
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Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

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