Renormalization group analysis of the 2000–2002 anti-bubble in the US S&P500 index: explanation of the hierarchy of five crashes and prediction

We propose a straightforward extension of our previously proposed log-periodic power-law model of the “anti-bubble” regime of the USA stock market since the summer of 2000, in terms of the renormalization group framework to model critical points. Using a previous work by Gluzman and Sornette (Phys. Rev. E 65 (2003) 036142) on the classification of the class of Weierstrass-like functions, we show that the five crashes that occurred since August 2000 can be accurately modeled by this approach, in a fully consistent way with no additional parameters. Our theory suggests an overall consistent organization of the investors forming a collective network which interact to form the pessimistic bearish “anti-bubble” regime with intermittent acceleration of the positive feedbacks of pessimistic sentiment leading to these crashes. We develop retrospective predictions, that confirm the existence of significant arbitrage opportunities for a trader using our model. Finally, we offer a prediction for the unknown future of the US S&P500 index extending over 2003 and 2004, that refines the previous prediction of Sornette and Zhou (Quant. Finance 2 (2002) 468).