Renormalization Group Analysis of the 2000-2002 anti-bubble in the US S&P 500 index: Explanation of the hierarchy of 5 crashes and Prediction

Wei-Xing Zhou and D. Sornette
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D. Sornette: CNRS-Univ. Nice and Ucla

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Abstract: We propose a straightforward extension of our previously proposed log-periodic power law model of the ``anti-bubble'' regime of the USA 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 (2002) on the classification of the class of Weierstrass-like functions, we show that the five crashes that occurred since August 2000 can be accurately modelled 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 (2002).

Date: 2003-01, Revised 2003-08
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Citations: View citations in EconPapers (18)

Published in Physica A 330 (2003) 584-604

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