ABSTRACT
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.
