Center for Polymer Studies and Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, USA.
Proc Natl Acad Sci U S A. 2011 May 10;108(19):7674-8. doi: 10.1073/pnas.1019484108. Epub 2011 Apr 26.
For an intriguing variety of switching processes in nature, the underlying complex system abruptly changes from one state to another in a highly discontinuous fashion. Financial market fluctuations are characterized by many abrupt switchings creating upward trends and downward trends, on time scales ranging from macroscopic trends persisting for hundreds of days to microscopic trends persisting for a few minutes. The question arises whether these ubiquitous switching processes have quantifiable features independent of the time horizon studied. We find striking scale-free behavior of the transaction volume after each switching. Our findings can be interpreted as being consistent with time-dependent collective behavior of financial market participants. We test the possible universality of our result by performing a parallel analysis of fluctuations in time intervals between transactions. We suggest that the well known catastrophic bubbles that occur on large time scales--such as the most recent financial crisis--may not be outliers but single dramatic representatives caused by the formation of increasing and decreasing trends on time scales varying over nine orders of magnitude from very large down to very small.
对于自然界中各种有趣的转变过程，基础复杂系统会以高度不连续的方式突然从一种状态转变为另一种状态。金融市场波动的特点是许多突然的转变，会产生上升趋势和下降趋势，时间尺度从持续数百天的宏观趋势到持续几分钟的微观趋势不等。问题是这些普遍存在的转变过程是否具有与所研究的时间范围无关的可量化特征。我们发现，在每次转变之后，交易量具有显著的无标度行为。我们的发现可以解释为与金融市场参与者的时变集体行为一致。我们通过对交易时间间隔波动进行平行分析来检验我们结果的可能普遍性。我们认为，在大时间尺度上发生的众所周知的灾难性泡沫——例如最近的金融危机——可能不是异常值，而是由时间尺度上的上升和下降趋势的形成引起的单一戏剧性代表，这些趋势的时间尺度跨越了九个数量级，从非常大到非常小。
