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# Financial Anti-Bubbles'': Log-Periodicity in Gold and Nikkei collapses

## Author

Listed:
• A. Johansen

(IGPP, UCLA)

• D. Sornette

(CNRS-University of Nice and UCLA)

## Abstract

We propose that imitation between traders and their herding behaviour not only lead to speculative bubbles with accelerating over-valuations of financial markets possibly followed by crashes, but also to anti-bubbles'' with decelerating market devaluations following all-time highs. For this, we propose a simple market dynamics model in which the demand decreases slowly with barriers that progressively quench in, leading to a power law decay of the market price decorated by decelerating log-periodic oscillations. We document this behaviour on the Japanese Nikkei stock index from 1990 to present and on the Gold future prices after 1980, both after their all-time highs. We perform simultaneously a parametric and non-parametric analysis that are fully consistent with each other. We extend the parametric approach to the next order of perturbation, comparing the log-periodic fits with one, two and three log-frequencies, the latter one providing a prediction for the general trend in the coming years. The non-parametric power spectrum analysis shows the existence of log-periodicity with high statistical significance, with a prefered scale ratio of $\lambda \approx 3.5$ for the Nikkei index $\lambda \approx 1.9$ for the Gold future prices, comparable to the values obtained for speculative bubbles leading to crashes.

## Suggested Citation

• A. Johansen & D. Sornette, 1999. "Financial Anti-Bubbles'': Log-Periodicity in Gold and Nikkei collapses," Papers cond-mat/9901268, arXiv.org.
• Handle: RePEc:arx:papers:cond-mat/9901268
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File URL: http://arxiv.org/pdf/cond-mat/9901268

## Citations

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Cited by:

1. V. Filimonov & G. Demos & D. Sornette, 2017. "Modified profile likelihood inference and interval forecast of the burst of financial bubbles," Quantitative Finance, Taylor & Francis Journals, vol. 17(8), pages 1167-1186, August.
2. Focardi, Sergio & Cincotti, Silvano & Marchesi, Michele, 2002. "Self-organization and market crashes," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 241-267, October.
3. Wei-Xing Zhou & Didier Sornette, 2005. "Fundamental Factors versus Herding in the 2000-2005 US Stock Market and Prediction," Papers physics/0505079, arXiv.org.
4. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Papers cond-mat/0106520, arXiv.org.
5. Ide, Kayo & Sornette, Didier, 2002. "Oscillatory finite-time singularities in finance, population and rupture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 307(1), pages 63-106.
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. Matsushita, Raul & da Silva, Sergio & Figueiredo, Annibal & Gleria, Iram, 2006. "Log-periodic crashes revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 331-335.
8. Lux, Thomas, 2008. "Applications of statistical physics in finance and economics," Kiel Working Papers 1425, Kiel Institute for the World Economy (IfW).
9. M. Ausloos & K. Ivanova & N. Vandewalle, 2001. "Crashes : symptoms, diagnoses and remedies," Papers cond-mat/0104127, arXiv.org, revised Apr 2001.
10. Thomas Lux, 2006. "Applications of Statistical Physics in Finance and Economics," Working Papers wpn06-07, Warwick Business School, Finance Group.
11. Fry, John, 2012. "Exogenous and endogenous crashes as phase transitions in complex financial systems," MPRA Paper 36202, University Library of Munich, Germany.
12. Zhi-Qiang Jiang & Wei-Xing Zhou & D. Sornette & Ryan Woodard & Ken Bastiaensen & Peter Cauwels, "undated". "Bubble Diagnosis and Prediction of the 2005-2007 and 2008-2009 Chinese stock market bubbles," Working Papers CCSS-09-008, ETH Zurich, Chair of Systems Design.
13. Zhou, Wei-Xing & Sornette, Didier, 2006. "Fundamental factors versus herding in the 2000–2005 US stock market and prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 459-482.
14. 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.
15. Fry, John & Cheah, Eng-Tuck, 2016. "Negative bubbles and shocks in cryptocurrency markets," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 343-352.
16. 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.
17. 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.
18. Maslov, Sergei & Roehner, Bertrand M, 2004. "The conundrum of stock versus bond prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 164-182.
19. 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.
20. 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.
21. Sornette, Didier & Woodard, Ryan & Zhou, Wei-Xing, 2009. "The 2006–2008 oil bubble: Evidence of speculation, and prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1571-1576.
22. Thomas Lux, 2009. "Applications of Statistical Physics in Finance and Economics," Chapters,in: Handbook of Research on Complexity, chapter 9 Edward Elgar Publishing.
23. Vogel, Harold L. & Werner, Richard A., 2015. "An analytical review of volatility metrics for bubbles and crashes," International Review of Financial Analysis, Elsevier, vol. 38(C), pages 15-28.
24. Anders Johansen & Didier Sornette, 2000. "The Nasdaq crash of April 2000: Yet another example of log-periodicity in a speculative bubble ending in a crash," Papers cond-mat/0004263, arXiv.org, revised May 2000.

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