英文标题：
《Transport catastrophe analysis as an alternative to a fractal
  description: theory and application to financial crisis time series》
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作者：
Sergey A. Kamenshchikov
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最新提交年份：
2014
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英文摘要：
  The goal of this investigation was to overcome limitations of a persistency analysis, introduced by Benoit Mandelbrot for fractal Brownian processes: nondifferentiability, Brownian nature of process and a linear memory measure. We have extended a sense of a Hurst factor by consideration of a phase diffusion power law. It was shown that pre-catastrophic stabilization as an indicator of bifurcation leads to a new minimum of momentary phase diffusion, while bifurcation causes an increase of the momentary transport. Basic conclusions of a diffusive analysis have been compared to the Lyapunov stability model. An extended Reynolds parameter has been introduces as an indicator of phase transition. A combination of diffusive and Reynolds analysis has been applied for a description of a time series of Dow Jones Industrial weekly prices for a world financial crisis of 2007-2009. Diffusive and Reynolds parameters shown an extreme values in October 2008 when a mortgage crisis was fixed. A combined R/D description allowed distinguishing of short-memory and long memory shifts of a market evolution. It was stated that a systematic large scale failure of a financial system has begun in October 2008 and started fading in February 2009.
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中文摘要：
本研究的目的是克服Benoit Mandelbrot为分形布朗过程引入的持久性分析的局限性：不可微性、过程的布朗性质和线性记忆度量。通过考虑相扩散幂律，我们扩展了赫斯特因子的意义。结果表明，作为分岔指标的灾前稳定会导致瞬时相扩散出现一个新的最小值，而分岔会导致瞬时输运的增加。将扩散分析的基本结论与李雅普诺夫稳定性模型进行了比较。引入了一个扩展的雷诺参数作为相变的指标。结合扩散分析和雷诺分析，对2007-2009年世界金融危机期间道琼斯工业周价格的时间序列进行了描述。扩散参数和雷诺参数在2008年10月抵押贷款危机修复时显示出极值。结合R/D描述，可以区分市场演变的短期记忆和长期记忆变化。据称，一个金融体系的系统性大规模失败始于2008年10月，并于2009年2月开始消退。
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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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