IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v490y2018icp834-844.html
   My bibliography  Save this article

Correlation between the Hurst exponent and the maximal Lyapunov exponent: Examining some low-dimensional conservative maps

Author

Listed:
  • Tarnopolski, Mariusz

Abstract

The Chirikov standard map and the 2D Froeschlé map are investigated. A few thousand values of the Hurst exponent (HE) and the maximal Lyapunov exponent (mLE) are plotted in a mixed space of the nonlinear parameter versus the initial condition. Both characteristic exponents reveal remarkably similar structures in this space. A tight correlation between the HEs and mLEs is found, with the Spearman rank ρ=0.83 and ρ=0.75 for the Chirikov and 2D Froeschlé maps, respectively. Based on this relation, a machine learning (ML) procedure, using the nearest neighbor algorithm, is performed to reproduce the HE distribution based on the mLE distribution alone. A few thousand HE and mLE values from the mixed spaces were used for training, and then using 2−2.4×105 mLEs, the HEs were retrieved. The ML procedure allowed to reproduce the structure of the mixed spaces in great detail.

Suggested Citation

  • Tarnopolski, Mariusz, 2018. "Correlation between the Hurst exponent and the maximal Lyapunov exponent: Examining some low-dimensional conservative maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 834-844.
    • Handle: RePEc:eee:phsmap:v:490:y:2018:i:c:p:834-844
    DOI: 10.1016/j.physa.2017.08.159
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117308920
    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.2017.08.159?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. Carbone, A. & Castelli, G. & Stanley, H.E., 2004. "Time-dependent Hurst exponent in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 267-271.
    2. Arianos, Sergio & Carbone, Anna, 2007. "Detrending moving average algorithm: A closed-form approximation of the scaling law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 9-15.
    3. Tarnopolski, Mariusz, 2016. "On the relationship between the Hurst exponent, the ratio of the mean square successive difference to the variance, and the number of turning points," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 662-673.
    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. McAllister, A. & McCartney, M. & Glass, D.H., 2023. "Stability, collapse and hyperchaos in a class of tri-trophic predator–prey models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 628(C).
    2. Wu, Xin & Shi, Hang & Ji’e, Musha & Duan, Shukai & Wang, Lidan, 2023. "A novel image compression and encryption scheme based on conservative chaotic system and DNA method," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    3. Xu, Beibei & Zhang, Jingjing & Egusquiza, Mònica & Chen, Diyi & Li, Feng & Behrens, Paul & Egusquiza, Eduard, 2021. "A review of dynamic models and stability analysis for a hydro-turbine governing system," Renewable and Sustainable Energy Reviews, Elsevier, vol. 144(C).
    4. McAllister, A. & McCartney, M. & Glass, D.H., 2024. "Correlation between Hurst exponent and largest Lyapunov exponent on a coupled map lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 641(C).
    5. Mihailović, Dragutin T. & Nikolić-Đorić, Emilija & Arsenić, Ilija & Malinović-Milićević, Slavica & Singh, Vijay P. & Stošić, Tatijana & Stošić, Borko, 2019. "Analysis of daily streamflow complexity by Kolmogorov measures and Lyapunov exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 290-303.

    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. Serletis, Apostolos & Rosenberg, Aryeh Adam, 2009. "Mean reversion in the US stock market," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2007-2015.
    2. Tarnopolski, Mariusz, 2016. "On the relationship between the Hurst exponent, the ratio of the mean square successive difference to the variance, and the number of turning points," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 662-673.
    3. Ni, Xiao-Hui & Jiang, Zhi-Qiang & Gu, Gao-Feng & Ren, Fei & Chen, Wei & Zhou, Wei-Xing, 2010. "Scaling and memory in the non-Poisson process of limit order cancelation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2751-2761.
    4. He, Ling-Yun & Chen, Shu-Peng, 2010. "Are developed and emerging agricultural futures markets multifractal? A comparative perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3828-3836.
    5. Ruan, Yong-Ping & Zhou, Wei-Xing, 2011. "Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1646-1654.
    6. Xie, Wen-Jie & Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2014. "Extreme value statistics and recurrence intervals of NYMEX energy futures volatility," Economic Modelling, Elsevier, vol. 36(C), pages 8-17.
    7. Jiang, Zhi-Qiang & Xie, Wen-Jie & Zhou, Wei-Xing, 2014. "Testing the weak-form efficiency of the WTI crude oil futures market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 235-244.
    8. Yue-Hua Dai & Wei-Xing Zhou, 2017. "Temporal and spatial correlation patterns of air pollutants in Chinese cities," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-24, August.
    9. Serinaldi, Francesco, 2010. "Use and misuse of some Hurst parameter estimators applied to stationary and non-stationary financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2770-2781.
    10. Zunino, Luciano & Tabak, Benjamin M. & Serinaldi, Francesco & Zanin, Massimiliano & Pérez, Darío G. & Rosso, Osvaldo A., 2011. "Commodity predictability analysis with a permutation information theory approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 876-890.
    11. Miguel Ángel Sánchez & Juan E Trinidad & José García & Manuel Fernández, 2015. "The Effect of the Underlying Distribution in Hurst Exponent Estimation," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-17, May.
    12. Serletis, Demitre, 2008. "Effect of noise on fractal structure," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 921-924.
    13. Gao, Xing-Lu & Shao, Ying-Hui & Yang, Yan-Hong & Zhou, Wei-Xing, 2022. "Do the global grain spot markets exhibit multifractal nature?," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    14. Juraj Čurpek, 2019. "Time Evolution of Hurst Exponent: Czech Wholesale Electricity Market Study," European Financial and Accounting Journal, Prague University of Economics and Business, vol. 2019(3), pages 25-44.
    15. Yuanyuan Zhang & Stephen Chan & Jeffrey Chu & Hana Sulieman, 2020. "On the Market Efficiency and Liquidity of High-Frequency Cryptocurrencies in a Bull and Bear Market," JRFM, MDPI, vol. 13(1), pages 1-14, January.
    16. Fernandez Viviana, 2011. "Alternative Estimators of Long-Range Dependence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-37, March.
    17. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    18. A. Gómez-Águila & J. E. Trinidad-Segovia & M. A. Sánchez-Granero, 2022. "Improvement in Hurst exponent estimation and its application to financial markets," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-21, December.
    19. He, Shanshan & Wang, Yudong, 2017. "Revisiting the multifractality in stock returns and its modeling implications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 11-20.
    20. Bariviera, A.F. & Guercio, M. Belén & Martinez, Lisana B., 2012. "A comparative analysis of the informational efficiency of the fixed income market in seven European countries," Economics Letters, Elsevier, vol. 116(3), pages 426-428.

    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:490:y:2018:i:c:p:834-844. 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.