Everything You Always Wanted to Know about Log Periodic Power Laws for Bubble Modelling but Were Afraid to Ask
Sornette et al. (1996), Sornette and Johansen (1997), Johansen et al. (2000) and Sornette (2003a) proposed that, prior to crashes, the mean function of a stock index price time series is characterized by a power law decorated with log-periodic oscillations, leading to a critical point that describes the beginning of the market crash. This paper reviews the original Log-Periodic Power Law (LPPL) model for financial bubble modelling, and discusses early criticism and recent generalizations proposed to answer these remarks. We show how to fit these models with alternative methodologies, together with diagnostic tests and graphical tools to diagnose financial bubbles in the making in real time. An application of this methodology to the Gold bubble which busted in December 2009 is then presented.
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- Zhou, Wei-Xing & Sornette, Didier, 2008. "Analysis of the real estate market in Las Vegas: Bubble, seasonal patterns, and prediction of the CSW indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 243-260.
- D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Papers cond-mat/0106520, arXiv.org.
- Carmen M. Reinhart & Kenneth S. Rogoff, 2009.
"Varieties of Crises and Their Dates,"
in: This Time Is Different: Eight Centuries of Financial Folly
Princeton University Press.
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8905, Michigan State - Econometrics and Economic Theory.
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- Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
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- L. Gazola & C. Fernandes & A. Pizzinga & R. Riera, 2008. "The log-periodic-AR(1)-GARCH(1,1) model for financial crashes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 61(3), pages 355-362, 02.
- 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.
- Zhou, Wei-Xing & Sornette, Didier, 2009. "A case study of speculative financial bubbles in the South African stock market 2003–2006," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 869-880.
- Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
- 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.
- L. Gazola & C. Fernandes & A. Pizzinga & R. Riera, 2008. "The log-periodic-AR(1)-GARCH(1,1) model for financial crashes," Papers 0801.4341, arXiv.org.
- Sornette, Didier & Zhou, Wei-Xing, 2006. "Predictability of large future changes in major financial indices," International Journal of Forecasting, Elsevier, vol. 22(1), pages 153-168.
- Johansen, Anders, 2003. "Characterization of large price variations in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 157-166.
- Dean Fantazzini, 2010. "Modelling and forecasting the global financial crisis: Initial findings using heterosckedastic log-periodic models," Economics Bulletin, AccessEcon, vol. 30(3), pages 1833-1841.
- Bauwens, Luc & Lubrano, Michel & Richard, Jean-Francois, 2000. "Bayesian Inference in Dynamic Econometric Models," OUP Catalogue, Oxford University Press, number 9780198773139, December.
- K. Bastiaensen & P. Cauwels & D. Sornette & R. Woodard & W. -X. Zhou, 2009. "The Chinese Equity Bubble: Ready to Burst," Papers 0907.1827, arXiv.org.
- D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, vol. 1(4), pages 452-471.
- Zhou, Wei-Xing & Sornette, Didier, 2006. "Is there a real-estate bubble in the US?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 297-308.
- D. Sornette, 2003. "Critical Market Crashes," Papers cond-mat/0301543, arXiv.org.
- Li LIN & Ruo En REN & Didier SORNETTE, 2009. "A Consistent Model of ‘Explosive’Financial Bubbles With Mean-Reversing Residuals," Swiss Finance Institute Research Paper Series 09-14, Swiss Finance Institute.
- Zhi-Qiang Jiang & Wei-Xing Zhou & Didier Sornette & Ryan Woodard & Ken Bastiaensen & Peter Cauwels, 2009. "Bubble Diagnosis and Prediction of the 2005-2007 and 2008-2009 Chinese stock market bubbles," Papers 0909.1007, arXiv.org, revised Oct 2009.
- W. -X. Zhou & D. Sornette, 2003. "2000-2003 Real Estate Bubble in the UK but not in the USA," Papers physics/0303028, arXiv.org, revised Jul 2003.
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