IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v558y2020ics0378437120305239.html
   My bibliography  Save this article

Binary indices of time series complexity measures and entropy plane

Author

Listed:
  • Shang, Binbin
  • Shang, Pengjian

Abstract

Complexity of time series is an important feature of dynamical systems such as financial systems. In order to bring out the complete non-linear behavior of financial time series, non-linear tools of complexity measurement like entropy measures are indispensable. Sample entropy (SampEn) and distribution entropy (DistEn) are popular methods of assessing the complexity in various fields. However, both sample entropy and distribution entropy show some limitations in detecting the complexity of stock markets. Therefore, we use two entropies as binary indices to analyze the complexity of time series and structure the entropy plane. In order to further improve the accuracy of the research results, we take the embedding dimension m as the variable, expand the entropy point into the entropy curve for further research. Furthermore, considering the shortcomings of sample entropy and distribution entropy in practical application, we generalize them by (i) replacing sample entropy and distribution entropy with multi-scale sample entropy and multi-scale distribution entropy; (ii) generalizing Shannon entropy as Tsallis entropy. Also, scale factor τ and entropic index q are taken respectively as variables to get the entropy curves. By using the artificial data, we confirm the rationality of using entropy points and entropy curves to study the complexity of time series. Finally, we apply this method to measure the complexity of real world financial time series, the results show that the entropy curves plotted by the financial time series obtained from different areas have significant differences.

Suggested Citation

  • Shang, Binbin & Shang, Pengjian, 2020. "Binary indices of time series complexity measures and entropy plane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    • Handle: RePEc:eee:phsmap:v:558:y:2020:i:c:s0378437120305239
    DOI: 10.1016/j.physa.2020.125003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437120305239
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2020.125003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, September.
    2. Gopikrishnan, P & Plerou, V & Liu, Y & Amaral, L.A.N & Gabaix, X & Stanley, H.E, 2000. "Scaling and correlation in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 362-373.
    3. Shi, Wenbin & Shang, Pengjian & Wang, Jing & Lin, Aijing, 2014. "Multiscale multifractal detrended cross-correlation analysis of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 35-44.
    4. Pierre Cizeau & Yanhui Liu & Martin Meyer & C. -K. Peng & H. Eugene Stanley, 1997. "Volatility distribution in the S&P500 Stock Index," Papers cond-mat/9708143, arXiv.org.
    5. Cizeau, Pierre & Liu, Yanhui & Meyer, Martin & Peng, C.-K. & Eugene Stanley, H., 1997. "Volatility distribution in the S&P500 stock index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 441-445.
    6. Borges, Ernesto P., 2004. "A possible deformed algebra and calculus inspired in nonextensive thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 95-101.
    7. Jauregui, M. & Zunino, L. & Lenzi, E.K. & Mendes, R.S. & Ribeiro, H.V., 2018. "Characterization of time series via Rényi complexity–entropy curves," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 498(C), pages 74-85.
    8. Rosenow, Bernd & Gopikrishnan, Parameswaran & Plerou, Vasiliki & Eugene Stanley, H, 2003. "Dynamics of cross-correlations in the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 241-246.
    9. L. Kullmann & J. Kertesz & K. Kaski, 2002. "Time dependent cross correlations between different stock returns: A directed network of influence," Papers cond-mat/0203256, arXiv.org, revised May 2002.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wan, Li & Ling, Guang & Guan, Zhi-Hong & Fan, Qingju & Tong, Yu-Han, 2022. "Fractional multiscale phase permutation entropy for quantifying the complexity of nonlinear time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    2. Wei, Nan & Yin, Lihua & Li, Chao & Liu, Jinyuan & Li, Changjun & Huang, Yuanyuan & Zeng, Fanhua, 2022. "Data complexity of daily natural gas consumption: Measurement and impact on forecasting performance," Energy, Elsevier, vol. 238(PC).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yang, Yujun & Li, Jianping & Yang, Yimei, 2017. "The cross-correlation analysis of multi property of stock markets based on MM-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 23-33.
    2. Shi, Wenbin & Shang, Pengjian & Wang, Jing & Lin, Aijing, 2014. "Multiscale multifractal detrended cross-correlation analysis of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 35-44.
    3. Shi, Wenbin & Shang, Pengjian & Xia, Jianan & Yeh, Chien-Hung, 2016. "The coupling analysis between stock market indices based on permutation measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 222-231.
    4. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: I. Empirical facts," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 991-1012.
    5. Łukasz Bil & Dariusz Grech & Magdalena Zienowicz, 2017. "Asymmetry of price returns—Analysis and perspectives from a non-extensive statistical physics point of view," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-24, November.
    6. Lin, Aijing & Shang, Pengjian & Zhong, Bo, 2014. "Hidden cross-correlation patterns in stock markets based on permutation cross-sample entropy and PCA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 259-272.
    7. Li, Chao & Shang, Pengjian, 2018. "Complexity analysis based on generalized deviation for financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 118-128.
    8. Mariani, M.C. & Florescu, I. & Beccar Varela, M.P. & Ncheuguim, E., 2010. "Study of memory effects in international market indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1653-1664.
    9. Schinckus, C., 2013. "Between complexity of modelling and modelling of complexity: An essay on econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3654-3665.
    10. Kim, Kyungwon & Jung, Sean S., 2014. "Empirical analysis of structural change in Credit Default Swap volatility," Chaos, Solitons & Fractals, Elsevier, vol. 60(C), pages 56-67.
    11. Mahata, Ajit & Bal, Debi Prasad & Nurujjaman, Md, 2020. "Identification of short-term and long-term time scales in stock markets and effect of structural break," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    12. Mariani, M.C. & Libbin, J.D. & Kumar Mani, V. & Beccar Varela, M.P. & Erickson, C.A. & Valles-Rosales, D.J., 2008. "Long correlations and Normalized Truncated Levy Models applied to the study of Indian Market Indices in comparison with other emerging markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1273-1282.
    13. David, S.A. & Inácio, C.M.C. & Quintino, D.D. & Machado, J.A.T., 2020. "Measuring the Brazilian ethanol and gasoline market efficiency using DFA-Hurst and fractal dimension," Energy Economics, Elsevier, vol. 85(C).
    14. Ko, Bonggyun & Song, Jae Wook, 2018. "A simple analytics framework for evaluating mean escape time in different term structures with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 398-412.
    15. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: II. Agent-based models," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1013-1041.
    16. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: I. Empirical facts," Post-Print hal-00621058, HAL.
    17. Yin, Yi & Shang, Pengjian, 2013. "Modified DFA and DCCA approach for quantifying the multiscale correlation structure of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6442-6457.
    18. S. M. Duarte Queiros, 2005. "On non-Gaussianity and dependence in financial time series: a nonextensive approach," Quantitative Finance, Taylor & Francis Journals, vol. 5(5), pages 475-487.
    19. Muchnik, Lev & Bunde, Armin & Havlin, Shlomo, 2009. "Long term memory in extreme returns of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4145-4150.
    20. Arthur Matsuo Yamashita Rios de Sousa & Hideki Takayasu & Misako Takayasu, 2017. "Detection of statistical asymmetries in non-stationary sign time series: Analysis of foreign exchange data," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-18, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:558:y:2020:i:c:s0378437120305239. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.