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Multiscale multifractal diffusion entropy analysis of financial time series

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  • Huang, Jingjing
  • Shang, Pengjian

Abstract

This paper introduces a multiscale multifractal diffusion entropy analysis (MMDEA) method to analyze long-range correlation then applies this method to stock index series. The method combines the techniques of diffusion process and Rényi entropy to focus on the scaling behaviors of stock index series using a multiscale, which allows us to extend the description of stock index variability to include the dependence on the magnitude of the variability and time scale. Compared to multifractal diffusion entropy analysis, the MMDEA can show more details of scale properties and provide a reliable analysis. In this paper, we concentrate not only on the fact that the stock index series has multifractal properties but also that these properties depend on the time scale in which the multifractality is measured. This time scale is related to the frequency band of the signal. We find that stock index variability appears to be far more complex than reported in the studies using a fixed time scale.

Suggested Citation

  • Huang, Jingjing & Shang, Pengjian, 2015. "Multiscale multifractal diffusion entropy analysis of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 221-228.
    • Handle: RePEc:eee:phsmap:v:420:y:2015:i:c:p:221-228
    DOI: 10.1016/j.physa.2014.11.009
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    References listed on IDEAS

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    1. Morales, Raffaello & Di Matteo, T. & Gramatica, Ruggero & Aste, Tomaso, 2012. "Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3180-3189.
    2. B. Podobnik & D. F. Fu & H. E. Stanley & P. Ch. Ivanov, 2007. "Power-law autocorrelated stochastic processes with long-range cross-correlations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 56(1), pages 47-52, March.
    3. Huang, Jingjing & Shang, Pengjian & Zhao, Xiaojun, 2012. "Multifractal diffusion entropy analysis on stock volatility in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5739-5745.
    4. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
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    Cited by:

    1. Guedes, E.F. & da Silva Filho, A.M. & Zebende, G.F., 2021. "Detrended multiple cross-correlation coefficient with sliding windows approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    2. He, Qian & Huang, Jingjing, 2020. "A method for analyzing correlation between multiscale and multivariate systems—Multiscale multidimensional cross recurrence quantification (MMDCRQA)," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Yang, Pengbo & Shang, Pengjian & Lin, Aijing, 2017. "Financial time series analysis based on effective phase transfer entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 398-408.
    4. Partida, Alberto & Gerassis, Saki & Criado, Regino & Romance, Miguel & Giráldez, Eduardo & Taboada, Javier, 2022. "The chaotic, self-similar and hierarchical patterns in Bitcoin and Ethereum price series," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    5. Dai, Meifeng & Hou, Jie & Gao, Jianyu & Su, Weiyi & Xi, Lifeng & Ye, Dandan, 2016. "Mixed multifractal analysis of China and US stock index series," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 268-275.

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