IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v392y2013i1p7-16.html
   My bibliography  Save this article

Multifractal models via products of geometric OU-processes: Review and applications

Author

Listed:
  • Leonenko, Nikolai
  • Petherick, Stuart
  • Taufer, Emanuele

Abstract

This paper reviews a class of multifractal models obtained via products of exponential Ornstein–Uhlenbeck processes driven by Lévy motion. Given a self-decomposable distribution, conditions for constructing multifractal scenarios and general formulas for their Renyi functions are provided. Together with several examples, a model with multifractal activity time is discussed and an application to exchange data is presented.

Suggested Citation

  • Leonenko, Nikolai & Petherick, Stuart & Taufer, Emanuele, 2013. "Multifractal models via products of geometric OU-processes: Review and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 7-16.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:1:p:7-16
    DOI: 10.1016/j.physa.2012.08.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437112008060
    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.2012.08.013?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. Taufer, Emanuele & Leonenko, Nikolai & Bee, Marco, 2011. "Characteristic function estimation of Ornstein-Uhlenbeck-based stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2525-2539, August.
    2. Robert J. Elliott & John Van Der Hoek, 2003. "A General Fractional White Noise Theory And Applications To Finance," Mathematical Finance, Wiley Blackwell, vol. 13(2), pages 301-330, April.
    3. 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.
    4. Gu, Rongbao & Chen, Hongtao & Wang, Yudong, 2010. "Multifractal analysis on international crude oil markets based on the multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2805-2815.
    5. Cajueiro, Daniel O. & Tabak, Benjamin M., 2007. "Long-range dependence and multifractality in the term structure of LIBOR interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 603-614.
    6. 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.
    7. 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.
    8. Wang, Yudong & Wei, Yu & Wu, Chongfeng, 2011. "Analysis of the efficiency and multifractality of gold markets based on multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 817-827.
    9. François Schmitt & Daniel Schertzer & Shaun Lovejoy, 1999. "Multifractal analysis of foreign exchange data," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 15(1), pages 29-53, March.
    10. Emanuele Taufer, 2008. "Characteristic function estimation of non-Gaussian Ornstein-Uhlenbeck processes," DISA Working Papers 0805, Department of Computer and Management Sciences, University of Trento, Italy, revised 07 Jul 2008.
    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. Grahovac, Danijel & Leonenko, Nikolai N., 2014. "Detecting multifractal stochastic processes under heavy-tailed effects," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 78-89.
    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.

    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. 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.
    2. 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.
    3. Nikolai Leonenko & EStuart Petherick & EmanueleTaufer, 2012. "Multifractal Scaling for Risky Asset Modelling," DISA Working Papers 2012/07, Department of Computer and Management Sciences, University of Trento, Italy, revised Jul 2012.
    4. R. P. Datta, 2023. "Analysis of Indian foreign exchange markets: A Multifractal Detrended Fluctuation Analysis (MFDFA) approach," Papers 2306.16162, arXiv.org.
    5. 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.
    6. Zhuang, Xiaoyang & Wei, Yu & Ma, Feng, 2015. "Multifractality, efficiency analysis of Chinese stock market and its cross-correlation with WTI crude oil price," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 101-113.
    7. Xiao, Di & Wang, Jun, 2021. "Attitude interaction for financial price behaviours by contact system with small-world network topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    8. Laura Raisa Miloş & Cornel Haţiegan & Marius Cristian Miloş & Flavia Mirela Barna & Claudiu Boțoc, 2020. "Multifractal Detrended Fluctuation Analysis (MF-DFA) of Stock Market Indexes. Empirical Evidence from Seven Central and Eastern European Markets," Sustainability, MDPI, vol. 12(2), pages 1-15, January.
    9. 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.
    10. Argyroudis, G. & Siokis, F., 2018. "The complexity of the HANG SENG Index and its constituencies during the 2007–2008 Great Recession," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 463-474.
    11. Rodriguez-Romo, Suemi & Sosa-Herrera, Antonio, 2013. "Lacunarity and multifractal analysis of the large DLA mass distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(16), pages 3316-3328.
    12. Barunik, Jozef & Aste, Tomaso & Di Matteo, T. & Liu, Ruipeng, 2012. "Understanding the source of multifractality in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(17), pages 4234-4251.
    13. 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 - AGER, vol. 0(3(632), A), pages 61-80, Autumn.
    14. Grahovac, Danijel & Leonenko, Nikolai N., 2014. "Detecting multifractal stochastic processes under heavy-tailed effects," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 78-89.
    15. 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.
    16. Saâdaoui, Foued, 2018. "Testing for multifractality of Islamic stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 263-273.
    17. 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.
    18. Lin, Xiaoqiang & Tang, Zhenpeng & Fei, Fangyu, 2013. "Testing for relationships between Shanghai and Shenzhen stock markets: A threshold cointegration perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 4064-4074.
    19. Zhou, Yaping & Lu, Baoqun & Lv, Dayong & Ruan, Qingsong, 2019. "The informativeness of options-trading activities: Non-linear analysis based on MF-DCCA and Granger test," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    20. Kyaw, NyoNyo A. & Los, Cornelis A. & Zong, Sijing, 2006. "Persistence characteristics of Latin American financial markets," Journal of Multinational Financial Management, Elsevier, vol. 16(3), pages 269-290, July.

    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:392:y:2013:i:1:p:7-16. 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.