标准普尔500指数US 2000-2002年反泡沫的重整化群分析：5次崩溃的层次解释和预测
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
摘要：
我们提出了一个简单的扩展，我们以前提出的对数周期幂律模型的"反泡沫“制度的美国市场自2000年夏天以来，在重整化群框架来模拟临界点。使用Gluzman和Sornette（2002）关于类维尔斯特拉斯函数分类的先前工作，我们表明，自2000年8月以来发生的五起撞车事故可以用这种方法准确建模，完全一致，没有额外的参数。我们的理论表明，投资者形成一个整体一致的组织，形成一个集体网络，相互作用，形成悲观看跌的“反泡沫”制度，间歇性加速悲观情绪的正反馈，导致这些崩溃。我们开发了回顾性预测，证实了使用我们的模型的交易者存在重大套利机会。最后，我们对2003年和2004年美国标准普尔500指数的未知未来进行了预测，改进了Sornette和Zhou（2002）的预测。
英文摘要：
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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