IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v394y2014icp226-234.html
   My bibliography  Save this article

Multifractality and long memory of a financial index

Author

Listed:
  • Suárez-García, Pablo
  • Gómez-Ullate, David

Abstract

In this paper we will try to assess the multifractality displayed by the high-frequency returns of Madrid’s Stock Exchange Ibex35 index. A Multifractal Detrended Fluctuation Analysis shows that this index has a wide singularity spectrum which is most likely caused by its long-memory. Our findings also show that this long-memory can be considered as the superposition of a high-frequency component–related to the daily cycles of arrival of information to the market–over a slowly-varying component that reverberates for long periods of time and which shows no apparent relation with human/economic cycles. This latter component is therefore postulated to be endogenous to market’s dynamics and to be also the most probable source of some of the stylized facts commonly associated with financial time-series.

Suggested Citation

  • Suárez-García, Pablo & Gómez-Ullate, David, 2014. "Multifractality and long memory of a financial index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 226-234.
    • Handle: RePEc:eee:phsmap:v:394:y:2014:i:c:p:226-234
    DOI: 10.1016/j.physa.2013.09.038
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437113009151
    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.2013.09.038?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. Turiel, Antonio & Pérez-Vicente, Conrad J., 2003. "Multifractal geometry in stock market time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 629-649.
    2. McCulloch, J Huston, 1997. "Measuring Tail Thickness to Estimate the Stable Index Alpha: A Critique," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 74-81, January.
    3. Thomas Lux, 2003. "The Multi-Fractal Model of Asset Returns:Its Estimation via GMM and Its Use for Volatility Forecasting," Computing in Economics and Finance 2003 14, Society for Computational Economics.
    4. 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.
    5. Laurent Calvet & Adlai Fisher, 2002. "Multifractality In Asset Returns: Theory And Evidence," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 381-406, August.
    6. Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1997. "Large Deviations and the Distribution of Price Changes," Cowles Foundation Discussion Papers 1165, Cowles Foundation for Research in Economics, Yale University.
    7. Zoltan Eisler & Janos Kertesz, 2004. "Multifractal model of asset returns with leverage effect," Papers cond-mat/0403767, arXiv.org, revised May 2004.
    8. Wei-Xing Zhou, 2009. "The components of empirical multifractality in financial returns," Papers 0908.1089, arXiv.org, revised Oct 2009.
    9. Y. Malevergne & V. Pisarenko & D. Sornette, 2005. "Empirical distributions of stock returns: between the stretched exponential and the power law?," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 379-401.
    10. 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.
    11. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    12. Wang, Hui & Xiang, Luojie & Pandey, R.B., 2012. "A multifractal detrended fluctuation analysis (MDFA) of the Chinese growth enterprise market (GEM)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3496-3502.
    13. Norouzzadeh, P. & Dullaert, W. & Rahmani, B., 2007. "Anti-correlation and multifractal features of Spain electricity spot market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 333-342.
    14. Petre Caraiani, 2012. "Evidence of Multifractality from Emerging European Stock Markets," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-9, July.
    15. Ivanova, K. & Shirer, H.N. & Clothiaux, E.E. & Kitova, N. & Mikhalev, M.A. & Ackerman, T.P. & Ausloos, M., 2002. "A case study of stratus cloud base height multifractal fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 308(1), pages 518-532.
    16. Ausloos, M., 2012. "Measuring complexity with multifractals in texts. Translation effects," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1349-1357.
    17. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-436, June.
    18. 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.
    19. Stanley, H.E. & Amaral, L.A.N. & Goldberger, A.L. & Havlin, S. & Ivanov, P.Ch. & Peng, C.-K., 1999. "Statistical physics and physiology: Monofractal and multifractal approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(1), pages 309-324.
    20. Eisler, Z. & Kertész, J., 2004. "Multifractal model of asset returns with leverage effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 603-622.
    21. B. B. Mandelbrot, 2001. "Scaling in financial prices: III. Cartoon Brownian motions in multifractal time," Quantitative Finance, Taylor & Francis Journals, vol. 1(4), pages 427-440.
    22. Adlai Fisher & Laurent Calvet & Benoit Mandelbrot, 1997. "Multifractality of Deutschemark/US Dollar Exchange Rates," Cowles Foundation Discussion Papers 1166, Cowles Foundation for Research in Economics, Yale University.
    23. Kantelhardt, Jan W & Koscielny-Bunde, Eva & Rego, Henio H.A & Havlin, Shlomo & Bunde, Armin, 2001. "Detecting long-range correlations with detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 441-454.
    24. Arneodo, A. & Audit, B. & Bacry, E. & Manneville, S. & Muzy, J.F. & Roux, S.G., 1998. "Thermodynamics of fractal signals based on wavelet analysis: application to fully developed turbulence data and DNA sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 254(1), pages 24-45.
    25. Suárez-García, Pablo & Gómez-Ullate, David, 2013. "Scaling, stability and distribution of the high-frequency returns of the Ibex35 index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1409-1417.
    26. Wei-Xing Zhou, 2008. "Multifractal detrended cross-correlation analysis for two nonstationary signals," Papers 0803.2773, arXiv.org.
    27. Xu, Zhaoxia & Gençay, Ramazan, 2003. "Scaling, self-similarity and multifractality in FX markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 578-590.
    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. Niu, Hongli & Wang, Jun, 2017. "Return volatility duration analysis of NYMEX energy futures and spot," Energy, Elsevier, vol. 140(P1), pages 837-849.
    2. Oumou Kalsoum Diallo & Pierre Mendy, 2019. "Wavelet Leader and Multifractal Detrended Fluctuation Analysis of Market Efficiency: Evidence from WAEMU Market Index," World Journal of Applied Economics, WERI-World Economic Research Institute, vol. 5(1), pages 1-23, June.
    3. Jasman Tuyon & Zamri Ahmada, 2016. "Behavioural finance perspectives on Malaysian stock market efficiency," Borsa Istanbul Review, Research and Business Development Department, Borsa Istanbul, vol. 16(1), pages 43-61, March.
    4. Niu, Hongli & Wang, Jun & Lu, Yunfan, 2016. "Fluctuation behaviors of financial return volatility duration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 30-40.
    5. Zhongjun Wang & Mengye Sun & A. M. Elsawah, 2020. "Improving MF-DFA model with applications in precious metals market," Papers 2006.15214, arXiv.org.

    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. Pablo Su'arez-Garc'ia & David G'omez-Ullate, 2013. "Multifractality and long memory of a financial index," Papers 1306.0490, arXiv.org.
    2. Akash P. POOJARI & Siva Kiran GUPTHA & G Raghavender RAJU, 2022. "Multifractal analysis of equities. Evidence from the emerging and frontier banking sectors," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(3(632), A), pages 61-80, Autumn.
    3. 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.
    4. 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.
    5. Fernández-Martínez, M. & Sánchez-Granero, M.A. & Casado Belmonte, M.P. & Trinidad Segovia, J.E., 2020. "A note on power-law cross-correlated processes," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    6. 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.
    7. 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.
    8. Onali, Enrico & Goddard, John, 2009. "Unifractality and multifractality in the Italian stock market," International Review of Financial Analysis, Elsevier, vol. 18(4), pages 154-163, September.
    9. 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.
    10. 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.
    11. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek, 2020. "Multiscale characteristics of the emerging global cryptocurrency market," Papers 2010.15403, arXiv.org, revised Mar 2021.
    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. El Alaoui, Marwane & Benbachir, Saâd, 2013. "Multifractal detrended cross-correlation analysis in the MENA area," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5985-5993.
    14. Tetsuya Takaishi, 2017. "Statistical properties and multifractality of Bitcoin," Papers 1707.07618, arXiv.org, revised May 2018.
    15. Caraiani, Petre & Haven, Emmanuel, 2015. "Evidence of multifractality from CEE exchange rates against Euro," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 395-407.
    16. Takaishi, Tetsuya, 2018. "Statistical properties and multifractality of Bitcoin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 507-519.
    17. Segnon, Mawuli & Lux, Thomas, 2013. "Multifractal models in finance: Their origin, properties, and applications," Kiel Working Papers 1860, Kiel Institute for the World Economy (IfW Kiel).
    18. Siokis, Fotios M., 2013. "Multifractal analysis of stock exchange crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1164-1171.
    19. 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.
    20. Deniz Erer & Elif Erer & Selim Güngör, 2023. "The aggregate and sectoral time-varying market efficiency during crisis periods in Turkey: a comparative analysis with COVID-19 outbreak and the global financial crisis," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-25, December.

    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:394:y:2014:i:c:p:226-234. 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.