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Irreversibility of financial time series: a graph-theoretical approach

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  • Lucas Lacasa
  • Ryan Flanagan

Abstract

The relation between time series irreversibility and entropy production has been recently investigated in thermodynamic systems operating away from equilibrium. In this work we explore this concept in the context of financial time series. We make use of visibility algorithms to quantify in graph-theoretical terms time irreversibility of 35 financial indices evolving over the period 1998-2012. We show that this metric is complementary to standard measures based on volatility and exploit it to both classify periods of financial stress and to rank companies accordingly. We then validate this approach by finding that a projection in principal components space of financial years based on time irreversibility features clusters together periods of financial stress from stable periods. Relations between irreversibility, efficiency and predictability are briefly discussed.

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  • Lucas Lacasa & Ryan Flanagan, 2016. "Irreversibility of financial time series: a graph-theoretical approach," Papers 1601.01980, arXiv.org.
    • Handle: RePEc:arx:papers:1601.01980
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    Cited by:

    1. Xiong, Hui & Shang, Pengjian & Xia, Jianan & Wang, Jing, 2018. "Time irreversibility and intrinsics revealing of series with complex network approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 241-249.
    2. Rong, Lei & Shang, Pengjian, 2018. "New irreversibility measure and complexity analysis based on singular value decomposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 913-924.
    3. Mao, Xuegeng & Shang, Pengjian, 2018. "Extended AIC model based on high order moments and its application in the financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 264-275.
    4. Jessica Morales Herrera & Ra'ul Salgado-Garc'ia, 2023. "Trend patterns statistics for assessing irreversibility in cryptocurrencies: time-asymmetry versus inefficiency," Papers 2307.08612, arXiv.org.
    5. Li, Jinyang & Shang, Pengjian, 2018. "Time irreversibility of financial time series based on higher moments and multiscale Kullback–Leibler divergence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 248-255.
    6. Wu, Zhenyu & Shang, Pengjian & Xiong, Hui, 2018. "An improvement of the measurement of time series irreversibility with visibility graph approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 370-378.
    7. Bai, Shiwei & Niu, Min, 2022. "The visibility graph of n-bonacci sequence," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    8. Flori, Andrea & Pammolli, Fabio & Spelta, Alessandro, 2021. "Commodity prices co-movements and financial stability: A multidimensional visibility nexus with climate conditions," Journal of Financial Stability, Elsevier, vol. 54(C).
    9. Huang, Yong & Yang, Dongqing & Wang, Lei & Wang, Kehong, 2020. "Classifying of welding time series based on multi-scale time irreversibility analysis and extreme learning machine," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    10. Xiong, Hui & Shang, Pengjian & He, Jiayi, 2019. "Nonuniversality of the horizontal visibility graph in inferring series periodicity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    11. Olivares, Felipe & Sun, Xiaoqian & Wandelt, Sebastian & Zanin, Massimiliano, 2023. "Measuring landing independence and interactions using statistical physics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 170(C).

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