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A stable and robust calibration scheme of the log-periodic power law model

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  • Filimonov, V.
  • Sornette, D.

Abstract

We present a simple transformation of the formulation of the log-periodic power law formula of the Johansen–Ledoit–Sornette (JLS) 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 the most crucial nonlinear parameter, the critical time tc, defined in the JLS model 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 a dramatic increase in efficiency. Empirical tests on the Shanghai Composite index (SSE) from January 2007 to March 2008 illustrate our findings.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:phsmap:v:392:y:2013:i:17:p:3698-3707
    DOI: 10.1016/j.physa.2013.04.012
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    References listed on IDEAS

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    Cited by:

    1. repec:eee:ememar:v:39:y:2019:i:c:p:120-132 is not listed on IDEAS
    2. Li, Chong, 2017. "Log-periodic view on critical dates of the Chinese stock market bubbles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 305-311.
    3. 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.
    4. 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, Publishing House "SINERGIA PRESS", vol. 44, pages 5-24.
    5. repec:spr:jeicoo:v:13:y:2018:i:2:d:10.1007_s11403-016-0187-7 is not listed on IDEAS
    6. repec:eee:eneeco:v:72:y:2018:i:c:p:341-355 is not listed on IDEAS
    7. 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.
    8. 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.
    9. repec:eee:phsmap:v:503:y:2018:i:c:p:947-957 is not listed on IDEAS
    10. repec:gam:jsusta:v:10:y:2018:i:12:p:4559-:d:187353 is not listed on IDEAS
    11. 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, Publishing House "SINERGIA PRESS", vol. 45, pages 5-28.
    12. repec:eee:phsmap:v:524:y:2019:i:c:p:661-675 is not listed on IDEAS
    13. 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.

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