dorsal/arxiv
View SchemaRenormalization Group Analysis of the 2000-2002 anti-bubble in the US S&P 500 index: Explanation of the hierarchy of 5 crashes and Prediction
| Authors | W. -X. Zhou, D. Sornette |
|---|---|
| Categories | |
| ArXiv ID | physics/0301023 |
| URL | https://arxiv.org/abs/physics/0301023 |
| DOI | 10.1016/j.physa.2003.09.022 |
| Journal | Physica A 330 (2003) 584-604 |
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).
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"abstract": "We propose a straightforward extension of our previously proposed\nlog-periodic power law model of the ``anti-bubble\u0027\u0027 regime of the USA market\nsince the summer of 2000, in terms of the renormalization group framework to\nmodel critical points. Using a previous work by Gluzman and Sornette (2002) on\nthe classification of the class of Weierstrass-like functions, we show that the\nfive crashes that occurred since August 2000 can be accurately modelled by this\napproach, in a fully consistent way with no additional parameters. Our theory\nsuggests an overall consistent organization of the investors forming a\ncollective network which interact to form the pessimistic bearish\n``anti-bubble\u0027\u0027 regime with intermittent acceleration of the positive feedbacks\nof pessimistic sentiment leading to these crashes. We develop retrospective\npredictions, that confirm the existence of significant arbitrage opportunities\nfor a trader using our model. Finally, we offer a prediction for the unknown\nfuture of the US S\u0026P500 index extending over 2003 and 2004, that refines the\nprevious prediction of Sornette and Zhou (2002).",
"arxiv_id": "physics/0301023",
"authors": [
"W. -X. Zhou",
"D. Sornette"
],
"categories": [
"physics.soc-ph",
"cond-mat.soft",
"physics.gen-ph",
"q-fin.GN"
],
"doi": "10.1016/j.physa.2003.09.022",
"journal_ref": "Physica A 330 (2003) 584-604",
"title": "Renormalization Group Analysis of the 2000-2002 anti-bubble in the US S\u0026P 500 index: Explanation of the hierarchy of 5 crashes and Prediction",
"url": "https://arxiv.org/abs/physics/0301023"
},
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