IDEAS home Printed from https://ideas.repec.org/p/stz/wpaper/eth-rc-11-002.html
   My bibliography  Save this paper

A Stable and Robust Calibration Scheme of the Log-Periodic Power Law Model

Author

Listed:
  • Vladimir Filimonov
  • Didier Sornette

Abstract

We present a simple transformation of the formulation of the log-periodic power law formula of the Johansen-Ledoit-Sornette model of financial bubbles that reduces it to a function of only three nonlinear parameters. The transformation significantly decreases the complexity of the fitting procedure and improves its stability tremendously because the modified cost function is now characterized by good smooth properties with in general a single minimum in the case where the model is appropriate to the empirical data. We complement the approach with an additional subordination procedure that slaves two of the nonlinear parameters to what can be considered to be the most crucial nonlinear parameter, the critical time tc defined as the end of the bubble and the most probable time for a crash to occur. This further decreases the complexity of the search and provides an intuitive representation of the results of the calibration. With our proposed methodology, metaheuristic searches are not longer necessary and one can resort solely to rigorous controlled local search algorithms, leading to dramatic increase in efficiency. Empirical tests on the Shanghai Composite index (SSE) from January 2007 to March 2008 illustrate our findings.

Suggested Citation

  • Vladimir Filimonov & Didier Sornette, "undated". "A Stable and Robust Calibration Scheme of the Log-Periodic Power Law Model," Working Papers ETH-RC-11-002, ETH Zurich, Chair of Systems Design.
    • Handle: RePEc:stz:wpaper:eth-rc-11-002
    as

    Download full text from publisher

    File URL: ftp://web.sg.ethz.ch/RePEc/stz/wpaper/pdf/ETH-RC-11-002.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Papers cond-mat/0106520, arXiv.org.
    2. J. Barkley Rosser Jr. (ed.), 2009. "Handbook of Research on Complexity," Books, Edward Elgar Publishing, number 3625.
    3. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, vol. 1(4), pages 452-471.
    4. Jiang, Zhi-Qiang & Zhou, Wei-Xing & Sornette, Didier & Woodard, Ryan & Bastiaensen, Ken & Cauwels, Peter, 2010. "Bubble diagnosis and prediction of the 2005-2007 and 2008-2009 Chinese stock market bubbles," Journal of Economic Behavior & Organization, Elsevier, vol. 74(3), pages 149-162, June.
    5. Anders Johansen & Didier Sornette, 2010. "Shocks, Crashes and Bubbles in Financial Markets," Brussels Economic Review, ULB -- Universite Libre de Bruxelles, vol. 53(2), pages 201-253.
    6. Anders Johansen & Olivier Ledoit & Didier Sornette, 2000. "Crashes As Critical Points," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 219-255.
    7. Sornette, Didier & Zhou, Wei-Xing, 2006. "Predictability of large future changes in major financial indices," International Journal of Forecasting, Elsevier, vol. 22(1), pages 153-168.
    8. J. Barkley Rosser, 2008. "Econophysics And Economic Complexity," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 11(05), pages 745-760.
    9. D. Sornette & R. Woodard, "undated". "Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis," Working Papers CCSS-09-003, ETH Zurich, Chair of Systems Design.
    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. Vladimir Filimonov & Didier Sornette, 2011. "A Stable and Robust Calibration Scheme of the Log-Periodic Power Law Model," Papers 1108.0099, arXiv.org, revised Jun 2013.
    2. Filimonov, V. & Sornette, D., 2013. "A stable and robust calibration scheme of the log-periodic power law model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3698-3707.
    3. Sornette, Didier & Woodard, Ryan & Yan, Wanfeng & Zhou, Wei-Xing, 2013. "Clarifications to questions and criticisms on the Johansen–Ledoit–Sornette financial bubble model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4417-4428.
    4. Wosnitza, Jan Henrik & Leker, Jens, 2014. "Can log-periodic power law structures arise from random fluctuations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 228-250.
    5. Lin, L. & Ren, R.E. & Sornette, D., 2014. "The volatility-confined LPPL model: A consistent model of ‘explosive’ financial bubbles with mean-reverting residuals," International Review of Financial Analysis, Elsevier, vol. 33(C), pages 210-225.
    6. Zhang, Qunzhi & Sornette, Didier & Balcilar, Mehmet & Gupta, Rangan & Ozdemir, Zeynel Abidin & Yetkiner, Hakan, 2016. "LPPLS bubble indicators over two centuries of the S&P 500 index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 126-139.
    7. Vakhtina, Elena & Wosnitza, Jan Henrik, 2015. "Capital market based warning indicators of bank runs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 304-320.
    8. Wosnitza, Jan Henrik & Denz, Cornelia, 2013. "Liquidity crisis detection: An application of log-periodic power law structures to default prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3666-3681.
    9. Fantazzini, Dean, 2016. "The oil price crash in 2014/15: Was there a (negative) financial bubble?," Energy Policy, Elsevier, vol. 96(C), pages 383-396.
    10. Cheng, Fangzheng & Fan, Tijun & Fan, Dandan & Li, Shanling, 2018. "The prediction of oil price turning points with log-periodic power law and multi-population genetic algorithm," Energy Economics, Elsevier, vol. 72(C), pages 341-355.
    11. Petr Geraskin & Dean Fantazzini, 2013. "Everything you always wanted to know about log-periodic power laws for bubble modeling but were afraid to ask," The European Journal of Finance, Taylor & Francis Journals, vol. 19(5), pages 366-391, May.
    12. Song, Ruiqiang & Shu, Min & Zhu, Wei, 2022. "The 2020 global stock market crash: Endogenous or exogenous?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    13. Fantazzini, Dean & Nigmatullin, Erik & Sukhanovskaya, Vera & Ivliev, Sergey, 2016. "Everything you always wanted to know about bitcoin modelling but were afraid to ask. I," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 44, pages 5-24.
    14. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    15. Gisler, Monika & Sornette, Didier & Woodard, Ryan, 2011. "Innovation as a social bubble: The example of the Human Genome Project," Research Policy, Elsevier, vol. 40(10), pages 1412-1425.
    16. Qun Zhang & Qunzhi Zhang & Didier Sornette, 2016. "Early Warning Signals of Financial Crises with Multi-Scale Quantile Regressions of Log-Periodic Power Law Singularities," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-43, November.
    17. Fantazzini, Dean & Nigmatullin, Erik & Sukhanovskaya, Vera & Ivliev, Sergey, 2017. "Everything you always wanted to know about bitcoin modelling but were afraid to ask. Part 2," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 45, pages 5-28.
    18. Didier Sornette & Ryan Woodard & Maxim Fedorovsky & Stefan Reimann & Hilary Woodard & Wei-Xing Zhou, 2009. "The Financial Bubble Experiment: advanced diagnostics and forecasts of bubble terminations," Papers 0911.0454, arXiv.org, revised May 2010.
    19. Maximilian Brauers & Matthias Thomas & Joachim Zietz, 2014. "Are There Rational Bubbles in REITs? New Evidence from a Complex Systems Approach," The Journal of Real Estate Finance and Economics, Springer, vol. 49(2), pages 165-184, August.
    20. Brée, David S. & Joseph, Nathan Lael, 2013. "Testing for financial crashes using the Log Periodic Power Law model," International Review of Financial Analysis, Elsevier, vol. 30(C), pages 287-297.

    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:stz:wpaper:eth-rc-11-002. 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: Claudio J. Tessone (email available below). General contact details of provider: https://edirc.repec.org/data/dmethch.html .

    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.