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.