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Time irreversibility of financial time series based on higher moments and multiscale Kullback–Leibler divergence

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  • Li, Jinyang
  • Shang, Pengjian

Abstract

Irreversibility is an important property of time series. In this paper, we propose the higher moments and multiscale Kullback–Leibler divergence to analyze time series irreversibility. The higher moments Kullback–Leibler divergence (HMKLD) can amplify irreversibility and make the irreversibility variation more obvious. Therefore, many time series whose irreversibility is hard to be found are also able to show the variations. We employ simulated data and financial stock data to test and verify this method, and find that HMKLD of stock data is growing in the form of fluctuations. As for multiscale Kullback–Leibler divergence (MKLD), it is very complex in the dynamic system, so that exploring the law of simulation and stock system is difficult. In conventional multiscale entropy method, the coarse-graining process is non-overlapping, however we apply a different coarse-graining process and obtain a surprising discovery. The result shows when the scales are 4 and 5, their entropy is nearly similar, which demonstrates MKLD is efficient to display characteristics of time series irreversibility.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:502:y:2018:i:c:p:248-255
    DOI: 10.1016/j.physa.2018.02.099
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    References listed on IDEAS

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    Cited by:

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    3. 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.

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