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Log-periodic self-similarity: an emerging financial law?

Author

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  • Drożdż, S.
  • Grümmer, F.
  • Ruf, F.
  • Speth, J.

Abstract

A hypothesis that the financial log-periodicity, cascading self-similarly through various time scales, carries signatures of a law is pursued. It is shown that the most significant historical financial events can be classified amazingly well using a single and unique value of the preferred scaling factor λ=2, which indicates that its real value should be close to this number. This applies even to a declining decelerating log-periodic phase. Crucial in this connection is identification of a “super-bubble” (bubble on bubble) phenomenon. Identifying a potential “universal” preferred scaling factor, as undertaken here, may significantly improve the predictive power of the corresponding methodology. Several more specific related results include evidence that: (i)the real end of the high technology bubble on the stock market started (with a decelerating log-periodic draw down) in the beginning of September 2000;(ii)a parallel 2000–2002 decline seen in the Standard & Poor's 500 from the log-periodic perspective is already of the same significance as the one of the early 1930s and of the late 1970s;(iii)all this points to a much more serious global crash in around 2025, of course from a level much higher (at least one order of magnitude) than in 2000.

Suggested Citation

  • Drożdż, S. & Grümmer, F. & Ruf, F. & Speth, J., 2003. "Log-periodic self-similarity: an emerging financial law?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 174-182.
    • Handle: RePEc:eee:phsmap:v:324:y:2003:i:1:p:174-182
    DOI: 10.1016/S0378-4371(02)01848-4
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    Citations

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    Cited by:

    1. Long, Yu, 2013. "Visibility graph network analysis of gold price time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(16), pages 3374-3384.
    2. James, Nick & Menzies, Max, 2023. "An exploration of the mathematical structure and behavioural biases of 21st century financial crises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    3. Stanis{l}aw Dro.zd.z & Rafa{l} Kowalski & Pawe{l} O'swic{e}cimka & Rafa{l} Rak & Robert Gc{e}barowski, 2018. "Dynamical variety of shapes in financial multifractality," Papers 1809.06728, arXiv.org.
    4. Zhou, Wei & Huang, Yang & Chen, Jin, 2018. "The bubble and anti-bubble risk resistance analysis on the metal futures in China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 947-957.
    5. Wosnitza, Jan Henrik & Leker, Jens, 2014. "Why credit risk markets are predestined for exhibiting log-periodic power law structures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 427-449.
    6. Ghosh, Koushik & Basu, Tapasendra, 2015. "Search for the periodicity of the prime Indian and American stock exchange indices using date-compensated discrete Fourier transformAuthor-Name: Samadder, Swetadri," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 149-157.
    7. Paweł Oświęcimka & Stanisław Drożdż & Jarosław Kwapień & Rafał Rak, 2011. "Is It Possible to Predict Crash?," Ekonomia journal, Faculty of Economic Sciences, University of Warsaw, vol. 25.
    8. Stanisław Drożdż & Jarosław Kwapień & Rafał Rak, 2011. "Characteristics of Financial Fluctuations," Ekonomia journal, Faculty of Economic Sciences, University of Warsaw, vol. 25.
    9. Aktham Maghyereh & Hussein Abdoh, 2022. "Bubble contagion effect between the main precious metals," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 40(1), pages 43-63, March.
    10. Wątorek Marcin & Stawiarski Bartosz, 2016. "Log-Periodic Power Law and Generalized Hurst Exponent Analysis in Estimating an Asset Bubble Bursting Time," Financial Internet Quarterly (formerly e-Finanse), Sciendo, vol. 12(3), pages 49-58, October.
    11. 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.
    12. 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.
    13. Białkowski, Jędrzej & Bohl, Martin T. & Stephan, Patrick M. & Wisniewski, Tomasz P., 2015. "The gold price in times of crisis," International Review of Financial Analysis, Elsevier, vol. 41(C), pages 329-339.
    14. Rodriguez, E. & Alvarez-Ramirez, J., 2021. "Time-varying cross-correlation between trading volume and returns in US stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    15. 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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