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

## Author Info

• A. Johansen

(IGPP, UCLA)

• D. Sornette

(CNRS-University of Nice and UCLA)

Registered author(s):

## 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.

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File URL: http://arxiv.org/pdf/cond-mat/9901268

## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number cond-mat/9901268.

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Publication status: Published in International Journal of Modern Physics C, Vol. 10, No. 4 (1999) 563-575
Handle: RePEc:arx:papers:cond-mat/9901268

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Web page: http://arxiv.org/

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## Citations

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Cited by:
1. Fantazzini, Dean & Geraskin, Petr, 2011. "Everything You Always Wanted to Know about Log Periodic Power Laws for Bubble Modelling but Were Afraid to Ask," MPRA Paper 47869, University Library of Munich, Germany.
2. Fry, John, 2012. "Exogenous and endogenous crashes as phase transitions in complex financial systems," MPRA Paper 36202, University Library of Munich, Germany.
3. Zhi-Qiang Jiang & Wei-Xing Zhou & D. Sornette & Ryan Woodard & Ken Bastiaensen & Peter Cauwels, . "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.
4. 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.
5. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Papers cond-mat/0106520, arXiv.org.
6. 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.
7. M. Ausloos & K. Ivanova & N. Vandewalle, 2001. "Crashes : symptoms, diagnoses and remedies," Papers cond-mat/0104127, arXiv.org, revised Apr 2001.
8. Wei-Xing Zhou & Didier Sornette, 2005. "Fundamental Factors versus Herding in the 2000-2005 US Stock Market and Prediction," Papers physics/0505079, arXiv.org.
9. 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.
10. 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.

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