IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v97y2017icp28-38.html
   My bibliography  Save this article

Asymmetric multi-fractality in the U.S. stock indices using index-based model of A-MFDFA

Author

Listed:
  • Lee, Minhyuk
  • Song, Jae Wook
  • Park, Ji Hwan
  • Chang, Woojin

Abstract

We detect the asymmetric multi-fractality in the U.S. stock indices based on the asymmetric multi-fractal detrended fluctuation analysis (A-MFDFA). Instead using the conventional return-based approach, we propose the index-based model of A-MFDFA where the trend based on the evolution of stock index rather than stock price return plays a role for evaluating the asymmetric scaling behaviors. The results show that the multi-fractal behaviors of the U.S. stock indices are asymmetric and the index-based model detects the asymmetric multi-fractality better than return-based model. We also discuss the source of multi-fractality and its asymmetry and observe that the multi-fractal asymmetry in the U.S. stock indices has a time-varying feature where the degree of multi-fractality and asymmetry increase during the financial crisis.

Suggested Citation

  • Lee, Minhyuk & Song, Jae Wook & Park, Ji Hwan & Chang, Woojin, 2017. "Asymmetric multi-fractality in the U.S. stock indices using index-based model of A-MFDFA," Chaos, Solitons & Fractals, Elsevier, vol. 97(C), pages 28-38.
    • Handle: RePEc:eee:chsofr:v:97:y:2017:i:c:p:28-38
    DOI: 10.1016/j.chaos.2017.02.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917300280
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2017.02.001?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. Lee, Jae Woo & Eun Lee, Kyoung & Arne Rikvold, Per, 2006. "Multifractal behavior of the Korean stock-market index KOSPI," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 355-361.
    2. Grech, D & Mazur, Z, 2004. "Can one make any crash prediction in finance using the local Hurst exponent idea?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 133-145.
    3. Alvarez-Ramirez, Jose & Rodriguez, Eduardo & Carlos Echeverria, Juan, 2009. "A DFA approach for assessing asymmetric correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(12), pages 2263-2270.
    4. Wei-Xing Zhou, 2009. "The components of empirical multifractality in financial returns," Papers 0908.1089, arXiv.org, revised Oct 2009.
    5. Cristescu, Constantin P. & Stan, Cristina & Scarlat, Eugen I. & Minea, Teofil & Cristescu, Cristina M., 2012. "Parameter motivated mutual correlation analysis: Application to the study of currency exchange rates based on intermittency parameter and Hurst exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2623-2635.
    6. Liang Ding & Hiroyoki Miyake & Hao Zou, 2011. "Asymmetric correlations in equity returns: a fundamental-based explanation," Applied Financial Economics, Taylor & Francis Journals, vol. 21(6), pages 389-399.
    7. Greene, Myron T. & Fielitz, Bruce D., 1977. "Long-term dependence in common stock returns," Journal of Financial Economics, Elsevier, vol. 4(3), pages 339-349, May.
    8. Zheng, Hongyang & Song, Weiguo & Wang, Jian, 2008. "Detrended fluctuation analysis of forest fires and related weather parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2091-2099.
    9. 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.
    10. 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.
    11. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
    12. Zhang, Chen & Ni, Zhiwei & Ni, Liping & Li, Jingming & Zhou, Longfei, 2016. "Asymmetric multifractal detrending moving average analysis in time series of PM2.5 concentration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 322-330.
    13. He, Ling-Yun & Chen, Shu-Peng, 2010. "Are crude oil markets multifractal? Evidence from MF-DFA and MF-SSA perspectives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3218-3229.
    14. 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.
    15. Wang, Yudong & Liu, Li & Gu, Rongbao & Cao, Jianjun & Wang, Haiyan, 2010. "Analysis of market efficiency for the Shanghai stock market over time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1635-1642.
    16. 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.
    17. Ivanova, K & Ausloos, M, 1999. "Application of the detrended fluctuation analysis (DFA) method for describing cloud breaking," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 349-354.
    18. Lee, Hojin & Song, Jae Wook & Chang, Woojin, 2016. "Multifractal Value at Risk model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 113-122.
    19. 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.
    20. 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.
    21. Wang, Yudong & Liu, Li & Gu, Rongbao, 2009. "Analysis of efficiency for Shenzhen stock market based on multifractal detrended fluctuation analysis," International Review of Financial Analysis, Elsevier, vol. 18(5), pages 271-276, December.
    22. Rivera-Castro, Miguel A. & Miranda, José G.V. & Cajueiro, Daniel O. & Andrade, Roberto F.S., 2012. "Detecting switching points using asymmetric detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 170-179.
    23. François Longin & Bruno Solnik, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
    24. Norouzzadeh, P. & Rahmani, B., 2006. "A multifractal detrended fluctuation description of Iranian rial–US dollar exchange rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 328-336.
    25. 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.
    26. Gao-Feng Gu & Wei-Xing Zhou, 2010. "Detrending moving average algorithm for multifractals," Papers 1005.0877, arXiv.org, revised Jun 2010.
    Full references (including those not matched with items on IDEAS)

    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. Gajardo, Gabriel & Kristjanpoller, Werner D. & Minutolo, Marcel, 2018. "Does Bitcoin exhibit the same asymmetric multifractal cross-correlations with crude oil, gold and DJIA as the Euro, Great British Pound and Yen?," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 195-205.
    2. 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.
    3. Lee, Minhyuk & Song, Jae Wook & Kim, Sondo & Chang, Woojin, 2018. "Asymmetric market efficiency using the index-based asymmetric-MFDFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1278-1294.
    4. 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.
    5. Mensi, Walid & Vo, Xuan Vinh & Kang, Sang Hoon, 2022. "Upward/downward multifractality and efficiency in metals futures markets: The impacts of financial and oil crises," Resources Policy, Elsevier, vol. 76(C).
    6. Chenyu Han & Yiming Wang & Yingying Xu, 2019. "Efficiency and Multifractality Analysis of the Chinese Stock Market: Evidence from Stock Indices before and after the 2015 Stock Market Crash," Sustainability, MDPI, vol. 11(6), pages 1-15, March.
    7. Wei, Yu & Wang, Yudong & Huang, Dengshi, 2011. "A copula–multifractal volatility hedging model for CSI 300 index futures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4260-4272.
    8. Mensi, Walid & Lee, Yun-Jung & Vinh Vo, Xuan & Yoon, Seong-Min, 2021. "Does oil price variability affect the long memory and weak form efficiency of stock markets in top oil producers and oil Consumers? Evidence from an asymmetric MF-DFA approach," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    9. Zhuang, Xiaoyang & Wei, Dan, 2022. "Asymmetric multifractality, comparative efficiency analysis of green finance markets: A dynamic study by index-based model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    10. Zhang, Chen & Ni, Zhiwei & Ni, Liping & Li, Jingming & Zhou, Longfei, 2016. "Asymmetric multifractal detrending moving average analysis in time series of PM2.5 concentration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 322-330.
    11. 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.
    12. 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.
    13. Zhou, Weijie & Dang, Yaoguo & Gu, Rongbao, 2013. "Efficiency and multifractality analysis of CSI 300 based on multifractal detrending moving average algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1429-1438.
    14. 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.
    15. Cao, Guangxi & Xu, Longbing & Cao, Jie, 2012. "Multifractal detrended cross-correlations between the Chinese exchange market and stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4855-4866.
    16. Choi, Sun-Yong, 2021. "Analysis of stock market efficiency during crisis periods in the US stock market: Differences between the global financial crisis and COVID-19 pandemic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    17. Wang, Qizhen & Zhu, Yingming & Yang, Liansheng & Mul, Remco A.H., 2017. "Coupling detrended fluctuation analysis of Asian stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 337-350.
    18. Zhang, Chen & Ni, Zhiwei & Ni, Liping, 2016. "Asymmetric multiscale behavior in PM2.5 time series: Based on asymmetric MS-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 355-365.
    19. Ruan, Qingsong & Bao, Junjie & Zhang, Manqian & Fan, Limin, 2019. "The effects of exchange rate regime reform on RMB markets: A new perspective based on MF-DCCA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 122-134.
    20. Naeem, Muhammad Abubakr & Farid, Saqib & Ferrer, Román & Shahzad, Syed Jawad Hussain, 2021. "Comparative efficiency of green and conventional bonds pre- and during COVID-19: An asymmetric multifractal detrended fluctuation analysis," Energy Policy, Elsevier, vol. 153(C).

    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:chsofr:v:97:y:2017:i:c:p:28-38. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.