IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v387y2008i2p511-518.html
   My bibliography  Save this article

Multifractal description of stock price index fluctuation using a quadratic function fitting

Author

Listed:
  • Yuan, Ying
  • Zhuang, Xin-tian

Abstract

In order to obtain a quantitative multifractal characterization of the stock price index, the multifractal spectrum of Shanghai stock price index time series in 2005 was investigated and the multifractal spectrum was fitted using a quadratic function. A sliding window of 240 frequency data in 5 trading days was used to investigate the stock price index fluctuation. The multifractal parameters and coefficients in each window were obtained by fitting the local multifractal spectrum using a quadratic function. It is found that when the stock price index fluctuates sharply, a strong variability is clearly characterized by the multifractal parameters and the quadratic function coefficients. This has led to a better understanding of complex stock markets.

Suggested Citation

  • Yuan, Ying & Zhuang, Xin-tian, 2008. "Multifractal description of stock price index fluctuation using a quadratic function fitting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 511-518.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:2:p:511-518
    DOI: 10.1016/j.physa.2007.09.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437107009934
    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.2007.09.015?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. B.H. Wang & P.M. Hui, 2001. "The distribution and scaling of fluctuations for Hang Seng index in Hong Kong stock market," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(4), pages 573-579, April.
    2. Sun, Xia & Chen, Huiping & Yuan, Yongzhuang & Wu, Ziqin, 2001. "Predictability of multifractal analysis of Hang Seng stock index in Hong Kong," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 473-482.
    3. Olan Henry, 2002. "Long memory in stock returns: some international evidence," Applied Financial Economics, Taylor & Francis Journals, vol. 12(10), pages 725-729.
    4. Sun, Xia & Chen, Huiping & Wu, Ziqin & Yuan, Yongzhuang, 2001. "Multifractal analysis of Hang Seng index in Hong Kong stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 291(1), pages 553-562.
    5. Wei, Yu & Huang, Dengshi, 2005. "Multifractal analysis of SSEC in Chinese stock market: A different empirical result from Heng Seng index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(2), pages 497-508.
    6. Skjeltorp, Johannes A, 2000. "Scaling in the Norwegian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(3), pages 486-528.
    7. Chen, Huiping & Sun, Xia & Wu, Ziqin & Wang, Binghong, 2004. "Enlightenment from various conditional probabilities about Hang Seng index in Hong Kong stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 183-196.
    8. Zhuang, Xin-tian & Huang, Xiao-yuan & Sha, Yan-li, 2004. "Research on the fractal structure in the Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 293-305.
    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. Li, Muyi & Huang, Yongxiang, 2014. "Hilbert–Huang Transform based multifractal analysis of China stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 222-229.
    2. Yufang Liu & Weiguo Zhang & Junhui Fu & Xiang Wu, 2020. "Multifractal Analysis of Realized Volatilities in Chinese Stock Market," Computational Economics, Springer;Society for Computational Economics, vol. 56(2), pages 319-336, August.
    3. Cao, Guangxi & Cao, Jie & Xu, Longbing, 2013. "Asymmetric multifractal scaling behavior in the Chinese stock market: Based on asymmetric MF-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 797-807.
    4. Hasan, Rashid & Mohammad, Salim M., 2015. "Multifractal analysis of Asian markets during 2007–2008 financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 746-761.
    5. Li, Jiang-Cheng & Tang, Nian-Sheng & Mei, Dong-Cheng & Li, Yun-Xian & Zhang, Wan, 2016. "The trading time risks of stock investment in stock price drop," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 778-787.
    6. Chen, Shu-Peng & He, Ling-Yun, 2010. "Multifractal spectrum analysis of nonlinear dynamical mechanisms in China’s agricultural futures markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1434-1444.
    7. Zhou, Wei-Xing, 2012. "Finite-size effect and the components of multifractality in financial volatility," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 147-155.
    8. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2008. "Multifractal analysis of Chinese stock volatilities based on the partition function approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4881-4888.
    9. 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.
    10. Qian, Xi-Yuan & Gu, Gao-Feng & Zhou, Wei-Xing, 2011. "Modified detrended fluctuation analysis based on empirical mode decomposition for the characterization of anti-persistent processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4388-4395.
    11. Yuan, Ying & Zhuang, Xin-tian & Jin, Xiu, 2009. "Measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(11), pages 2189-2197.
    12. Wei, Yu & Chen, Wang & Lin, Yu, 2013. "Measuring daily Value-at-Risk of SSEC index: A new approach based on multifractal analysis and extreme value theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2163-2174.
    13. Zhongjun Wang & Mengye Sun & A. M. Elsawah, 2020. "Improving MF-DFA model with applications in precious metals market," Papers 2006.15214, arXiv.org.
    14. Chen, Wang & Wei, Yu & Lang, Qiaoqi & Lin, Yu & Liu, Maojuan, 2014. "Financial market volatility and contagion effect: A copula–multifractal volatility approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 289-300.
    15. Yuan, Ying & Zhuang, Xin-tian & Liu, Zhi-ying, 2012. "Price–volume multifractal analysis and its application in Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3484-3495.

    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. Yuan, Ying & Zhuang, Xin-tian & Jin, Xiu, 2009. "Measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(11), pages 2189-2197.
    2. Yuan, Ying & Zhuang, Xin-tian & Liu, Zhi-ying, 2012. "Price–volume multifractal analysis and its application in Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3484-3495.
    3. Gu, Rongbao & Xiong, Wei & Li, Xinjie, 2015. "Does the singular value decomposition entropy have predictive power for stock market? — Evidence from the Shenzhen stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 439(C), pages 103-113.
    4. Wei, Yu & Chen, Wang & Lin, Yu, 2013. "Measuring daily Value-at-Risk of SSEC index: A new approach based on multifractal analysis and extreme value theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2163-2174.
    5. Chen, Hongtao & Wu, Chongfeng, 2011. "Forecasting volatility in Shanghai and Shenzhen markets based on multifractal analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(16), pages 2926-2935.
    6. Cajueiro, Daniel O. & Tabak, Benjamin M., 2006. "Testing for predictability in equity returns for European transition markets," Economic Systems, Elsevier, vol. 30(1), pages 56-78, March.
    7. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2008. "Multifractal analysis of Chinese stock volatilities based on the partition function approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4881-4888.
    8. Wei, Yu & Wang, Peng, 2008. "Forecasting volatility of SSEC in Chinese stock market using multifractal analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(7), pages 1585-1592.
    9. Chen, Wang & Wei, Yu & Lang, Qiaoqi & Lin, Yu & Liu, Maojuan, 2014. "Financial market volatility and contagion effect: A copula–multifractal volatility approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 289-300.
    10. Zhou, Wei-Xing, 2012. "Finite-size effect and the components of multifractality in financial volatility," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 147-155.
    11. Ho, Ding-Shun & Lee, Chung-Kung & Wang, Cheng-Cai & Chuang, Mang, 2004. "Scaling characteristics in the Taiwan stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 448-460.
    12. Bai, Man-Ying & Zhu, Hai-Bo, 2010. "Power law and multiscaling properties of the Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1883-1890.
    13. Rypdal, Martin & Sirnes, Espen & Løvsletten, Ola & Rypdal, Kristoffer, 2013. "Assessing market uncertainty by means of a time-varying intermittency parameter for asset price fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(16), pages 3335-3343.
    14. 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.
    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. 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.
    17. Yuan, Ying & Zhang, Tonghui, 2020. "Forecasting stock market in high and low volatility periods: a modified multifractal volatility approach," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    18. Xun Huang & Huiyue Tang, 2022. "Measuring multi‐volatility states of financial markets based on multifractal clustering model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(3), pages 422-434, April.
    19. Cajueiro, Daniel O. & Gogas, Periklis & Tabak, Benjamin M., 2009. "Does financial market liberalization increase the degree of market efficiency? The case of the Athens stock exchange," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 50-57, March.
    20. Zunino, Luciano & Figliola, Alejandra & Tabak, Benjamin M. & Pérez, Darío G. & Garavaglia, Mario & Rosso, Osvaldo A., 2009. "Multifractal structure in Latin-American market indices," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2331-2340.

    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:387:y:2008:i:2:p:511-518. 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.