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A Consistent Model of `Explosive' Financial Bubbles With Mean-Reversing Residuals

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  • L. Lin
  • Ren R. E
  • D. Sornette

Abstract

We present a self-consistent model for explosive financial bubbles, which combines a mean-reverting volatility process and a stochastic conditional return which reflects nonlinear positive feedbacks and continuous updates of the investors' beliefs and sentiments. The conditional expected returns exhibit faster-than-exponential acceleration decorated by accelerating oscillations, called "log-periodic power law." Tests on residuals show a remarkable low rate (0.2%) of false positives when applied to a GARCH benchmark. When tested on the S&P500 US index from Jan. 3, 1950 to Nov. 21, 2008, the model correctly identifies the bubbles ending in Oct. 1987, in Oct. 1997, in Aug. 1998 and the ITC bubble ending on the first quarter of 2000. Different unit-root tests confirm the high relevance of the model specification. Our model also provides a diagnostic for the duration of bubbles: applied to the period before Oct. 1987 crash, there is clear evidence that the bubble started at least 4 years earlier. We confirm the validity and universality of the volatility-confined LPPL model on seven other major bubbles that have occurred in the World in the last two decades. Using Bayesian inference, we find a very strong statistical preference for our model compared with a standard benchmark, in contradiction with Chang and Feigenbaum (2006) which used a unit-root model for residuals.

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  • L. Lin & Ren R. E & D. Sornette, 2009. "A Consistent Model of `Explosive' Financial Bubbles With Mean-Reversing Residuals," Papers 0905.0128, arXiv.org.
    • Handle: RePEc:arx:papers:0905.0128
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    References listed on IDEAS

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    1. George Chang & James Feigenbaum, 2006. "A Bayesian analysis of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 15-36.
    2. Anders Johansen, 2004. "Origin of Crashes in 3 US stock markets: Shocks and Bubbles," Papers cond-mat/0401210, arXiv.org.
    3. Johansen, Anders, 2004. "Origin of crashes in three US stock markets: shocks and bubbles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(1), pages 135-142.
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    Cited by:

    1. 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.
    2. 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.
    3. Hanousek, Jan & Novotný, Jan, 2012. "Price jumps in Visegrad-country stock markets: An empirical analysis," Emerging Markets Review, Elsevier, vol. 13(2), pages 184-201.
    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. Revant Nayar & Minhajul Islam, 2024. "Endogenous Crashes as Phase Transitions," Papers 2408.06433, arXiv.org.
    6. Siab Mamipour & Mahshid Sepahi, 2015. "Analysis of the Behavior of Amateur and Professional Investors’ Impact on the Formation of Bubbles in Tehran Stock Market," Iranian Economic Review (IER), Faculty of Economics,University of Tehran.Tehran,Iran, vol. 19(3), pages 341-358, Autumn.

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