Everything you always wanted to know about log-periodic power laws for bubble modeling but were afraid to ask

Sornette, Johansen, and Bouchaud (1996), Sornette and Johansen (1997), Johansen, Ledoit, and Sornette (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 article reviews the original log-periodic power law model for financial bubble modeling 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 burst in December 2009 is then presented.

[1]  D. Sornette.  Why Stock Markets Crash: Critical Events in Complex Financial Systems , 2017 .

[2]  Olivier Ledoit,et al.  CRASHES AS CRITICAL POINTS , 1998, cond-mat/9810071.

[3]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[4]  Jonathan D. Levin.  Bubbles and Crashes , 2006 .

[5]  O. Blanchard,et al.  Speculative bubbles, crashes and rational expectations , 1979 .

[6]  D. Sornette,et al.  Large financial crashes , 1997, cond-mat/9704127.

[7]  P. Phillips,et al.  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? , 1992 .

[8]  R. Gorvett.  Why Stock Markets Crash: Critical Events in Complex Financial Systems , 2005 .

[9]  D. Sornette,et al.  Testing the stability of the 2000 US stock market “antibubble” , 2005 .

[10]  J. Stock.  Unit roots, structural breaks and trends , 1986 .

[11]  H. Stanley,et al.  Introduction to Phase Transitions and Critical Phenomena , 1972 .

[12]  D. Sornette,et al.  Bubble Diagnosis and Prediction of the 2005-2007 and 2008-2009 Chinese Stock Market Bubbles , 2009, 0909.1007.

[13]  Mark W. Watson.  Introduction to econometrics. , 1968 .

[14]  Markus K. Brunnermeier,et al.  Bubbles and crashes , 2002 .

[15]  The 2006-2008 Oil Bubble and Beyond , 2008, 0806.1170.

[16]  Didier Sornette,et al.  A Consistent Model of 'Explosive' Financial Bubbles with Mean-Reversing Residuals , 2009, 0905.0128.

[17]  Didier Sornette,et al.  2000-2003 Real Estate Bubble in the UK but not in the USA , 2003 .

[18]  Bernhard Pfaff,et al.  Analysis of Integrated and Cointegrated Time Series with R , 2005 .

[19]  Eric R. Ziegel,et al.  Analysis of Financial Time Series , 2002, Technometrics.

[20]  Didier Sornette,et al.  Financial Anti-Bubbles Log-Periodicity in Gold and Nikkei Collapses , 1999, cond-mat/9901268.

[21]  Anders Johansen,et al.  Comment on “Are financial crashes predictable?” by L. Laloux, M. Potters, R. Cont, J.-P. Aguilar and J.-P. Bouchaud , 2002, cond-mat/0205249.

[22]  Didier Sornette,et al.  The 2006–2008 oil bubble: Evidence of speculation, and prediction , 2009 .

[23]  D. Sornette,et al.  Evaluation of the Quantitative Prediction of a Trend Reversal on the Japanese Stock Market in 1999 , 2000 .

[24]  David M. Tate,et al.  A genetic algorithm approach to curve fitting , 1995 .

[25]  J. Feigenbaum,et al.  A Bayesian analysis of log-periodic precursors to financial crashes , 2001 .

[26]  Didier Sornette,et al.  Shocks, Crashes and Bubbles in Financial Markets , 2010 .

[27]  D. Sornette.  Dragon-Kings, Black Swans and the Prediction of Crises , 2009, 0907.4290.

[28]  D. Sornette,et al.  Bubble Diagnosis and Prediction of the 2005-2007 and 2008-2009 Chinese Stock Market Bubbles , 2009 .

[29]  Bernard Derrida,et al.  Fractal structure of zeros in hierarchical models , 1983 .

[30]  Hersh Shefrin,et al.  A Behavioral Approach to Asset Pricing , 2005 .

[31]  V. Chernozhukov,et al.  Bayesian Econometrics , 2007 .

[32]  Didier Sornette,et al.  Analysis of the real estate market in Las Vegas: Bubble, seasonal patterns, and prediction of the CSW indices , 2007, 0704.0589.

[33]  Luc Bauwens,et al.  Bayesian Inference in Dynamic Econometric Models , 2000 .

[34]  Financial Bubbles, Real Estate Bubbles, Derivative Bubbles, and the Financial and Economic Crisis , 2009 .

[35]  Emilie Jacobsson,et al.  How to predict crashes in financial markets with the Log-Periodic Power Law , 2009 .

[36]  Didier Sornette,et al.  Financial Bubbles, Real Estate Bubbles, Derivative Bubbles, and the Financial and Economic Crisis , 2009, 0905.0220.

[37]  P. Perron,et al.  Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power , 2001 .

[38]  D Cvijovicacute,et al.  Taboo search: an approach to the multiple minima problem. , 1995, Science.

[39]  D. Sornette,et al.  Significance of log-periodic precursors to financial crashes , 2001, cond-mat/0106520.

[40]  Anders Johansen.  Characterization of large price variations in financial markets , 2003 .

[41]  William E. Griffiths,et al.  Using EViews for Principles of Econometrics , 2008 .

[42]  Didier Sornette,et al.  Diagnostics of rational expectation financial bubbles with stochastic mean-reverting termination times , 2009, New Facets of Economic Complexity in Modern Financial Markets.

[43]  R. H. Parker,et al.  This time is different: eight centuries of financial folly , 2010 .

[44]  R. Riera,et al.  The log-periodic-AR(1)-GARCH(1,1) model for financial crashes , 2008 .

[45]  Didier Sornette,et al.  A case study of speculative financial bubbles in the South African stock market 2003-2006 , 2007, physics/0701171.

[46]  Didier Sornette,et al.  Testing the Stability of the 2000-2003 Us Stock Market 'Antibubble' , 2003 .

[47]  Rama Cont,et al.  Are financial crashes predictable , 1999 .

[48]  N. Goldenfeld.  Lectures On Phase Transitions And The Renormalization Group , 1972 .

[49]  Dean Fantazzini,et al.  Modelling and Forecasting the Global Financial Crisis: Initial Findings Using Heterosckedastic Log-Periodic Models , 2009 .

[50]  D. Sornette,et al.  Predictability of large future changes in major financial indices , 2003, cond-mat/0304601.

[51]  Dean Fantazzini.  Modelling Bubbles and Anti-Bubbles in Bear Markets: A Medium-Term Trading Analysis , 2010 .

[52]  Didier Sornette,et al.  Critical Market Crashes , 2003, cond-mat/0301543.

[53]  D. Sornette,et al.  Stock Market Crashes, Precursors and Replicas , 1995, cond-mat/9510036.

[54]  Didier Sornette,et al.  Endogenous Versus Exogenous Crashes in Financial Markets , 2002 .

[55]  D. Sornette,et al.  Is there a real-estate bubble in the US? , 2005, physics/0506027.

[56]  L. Onsager.  Crystal statistics. I. A two-dimensional model with an order-disorder transition , 1944 .

[57]  R. Gürkaynak.  Econometric Tests of Asset Price Bubbles: Taking Stock , 2005 .

[58]  Didier Sornette,et al.  The Chinese Equity Bubble: Ready to Burst , 2009 .