IDEAS home Printed from https://ideas.repec.org/p/arx/papers/physics-0609210.html
   My bibliography  Save this paper

Scale invariant multiplier and multifractality of absolute returns in stock markets

Author

Listed:
  • Zhi-Qiang Jiang

    (ECUST)

  • Wei-Xing Zhou

    (ECUST)

Abstract

The statistical properties of the multipliers of the absolute returns are investigated using one-minute high-frequency data of financial time series. The multiplier distribution is found to be independent of the box size $s$ when $s$ is larger than some crossover scale, providing direct evidence of the existence of scale invariance in financial data. The multipliers with base $a=2$ are well approximated by a normal distribution and the most probable multiplier scales as a power law in respect to the base $a$. We unravel that the volatility multipliers possess multifractal nature which is independent of construction of the multipliers, that is, the values of $s$ and $a$.

Suggested Citation

  • Zhi-Qiang Jiang & Wei-Xing Zhou, 2006. "Scale invariant multiplier and multifractality of absolute returns in stock markets," Papers physics/0609210, arXiv.org, revised Feb 2007.
  • Handle: RePEc:arx:papers:physics/0609210
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/physics/0609210
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Muniandy, S.V. & Lim, S.C. & Murugan, R., 2001. "Inhomogeneous scaling behaviors in Malaysian foreign currency exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 407-428.
    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. Dewandaru, Ginanjar & Masih, Rumi & Bacha, Obiyathulla Ismath & Masih, A. Mansur. M., 2015. "Developing trading strategies based on fractal finance: An application of MF-DFA in the context of Islamic equities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 223-235.
    2. Rizvi, Syed Aun R. & Dewandaru, Ginanjar & Bacha, Obiyathulla I. & Masih, Mansur, 2014. "An analysis of stock market efficiency: Developed vs Islamic stock markets using MF-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 86-99.

    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. Wang, Dong-Hua & Yu, Xiao-Wen & Suo, Yuan-Yuan, 2012. "Statistical properties of the yuan exchange rate index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3503-3512.
    2. Wang, Gang-Jin & Xie, Chi, 2013. "Cross-correlations between Renminbi and four major currencies in the Renminbi currency basket," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1418-1428.
    3. Li, Ming, 2020. "Multi-fractional generalized Cauchy process and its application to teletraffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    4. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    5. Dutta, Srimonti & Ghosh, Dipak & Samanta, Shukla, 2014. "Multifractal detrended cross-correlation analysis of gold price and SENSEX," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 195-204.
    6. Song, Wanqing & Cattani, Carlo & Chi, Chi-Hung, 2020. "Multifractional Brownian motion and quantum-behaved particle swarm optimization for short term power load forecasting: An integrated approach," Energy, Elsevier, vol. 194(C).
    7. Sukpitak, Jessada & Hengpunya, Varagorn, 2016. "The influence of trading volume on market efficiency: The DCCA approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 259-265.
    8. Li, Ming & Sun, Xichao & Xiao, Xi, 2019. "Revisiting fractional Gaussian noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 56-62.
    9. Wang, Xiao-Tian, 2011. "Scaling and long-range dependence in option pricing V: Multiscaling hedging and implied volatility smiles under the fractional Black–Scholes model with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1623-1634.
    10. M. Bartolozzi & C. Mellen, 2009. "Local Risk Decomposition for High-frequency Trading Systems," Papers 0904.4099, arXiv.org, revised Feb 2011.
    11. Li, Ming & Zhao, Wei, 2012. "Quantitatively investigating the locally weak stationarity of modified multifractional Gaussian noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6268-6278.
    12. R. P. Datta, 2023. "Analysis of Indian foreign exchange markets: A Multifractal Detrended Fluctuation Analysis (MFDFA) approach," Papers 2306.16162, arXiv.org.
    13. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2008. "Multifractality in stock indexes: Fact or Fiction?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3605-3614.
    14. Wang, Xiao-Tian, 2010. "Scaling and long range dependence in option pricing, IV: Pricing European options with transaction costs under the multifractional Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 789-796.
    15. Du, Guoxiong & Ning, Xuanxi, 2008. "Multifractal properties of Chinese stock market in Shanghai," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 261-269.
    16. Dutta, Srimonti & Ghosh, Dipak & Chatterjee, Sucharita, 2016. "Multifractal detrended Cross Correlation Analysis of Foreign Exchange and SENSEX fluctuation in Indian perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 188-201.
    17. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2007. "Scale invariant distribution and multifractality of volatility multipliers in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 343-350.
    18. Grobys, Klaus, 2023. "A Fractal and Comparative View of the Memory of Bitcoin and S&P 500 Returns," Research in International Business and Finance, Elsevier, vol. 66(C).
    19. Wang, Yudong & Wu, Chongfeng & Pan, Zhiyuan, 2011. "Multifractal detrending moving average analysis on the US Dollar exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3512-3523.
    20. Abounoori, Esmaiel & Shahrazi, Mahdi & Rasekhi, Saeed, 2012. "An investigation of Forex market efficiency based on detrended fluctuation analysis: A case study for Iran," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3170-3179.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:physics/0609210. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.