摘要翻译：
我们把崩盘前的市场价格（纳斯达克，道琼斯工业平均指数）作为一个信号，一个时间的函数，我们把这些离散的值投射到一个垂直轴上，从而得到一个cantordust。我们用多重分形分析的工具研究了said cantordust，通过定义和拉格朗日坐标获得了光谱。这些光谱具有典型的崩盘前市场情况的性质。任何这些光谱都需要对原始信号数据进行精心处理。利用未经处理的原始数据，我们得到了一个不稳定性指数，该指数也具有典型的危机前市场状况的性质。光谱和不稳定指数在描述这种碰撞和对它们发出早期预警方面都是一致的。
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英文标题：
《Multifractal analysis and instability index of prior-to-crash market
  situations》
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作者：
M. Piacquadio and F. O. Redelico
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最新提交年份：
2009
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Mathematics        数学
二级分类：Numerical Analysis        数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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英文摘要：
  We take prior-to-crash market prices (NASDAQ, Dow Jones Industrial Average) as a signal, a function of time, we project these discrete values onto a vertical axis, thus obtaining a Cantordust. We study said cantordust with the tools of multifractal analysis, obtaining spectra by definition and by lagrangian coordinates. These spectra have properties that typify the prior-to-crash market situation. Any of these spectra entail elaborate processing of the raw signal data. With the unprocessed raw data we obtain an instability index, also with properties that typify the prior-to-crisis market situation. Both spectra and the instability index agree in characterizing such crashes, and in giving an early warning of them.
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PDF链接：
https://arxiv.org/pdf/0910.2474