Topological data analysis of financial time series: Landscapes of crashes
Topological data analysis of financial time series: Landscapes of crashes
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DOI：
10.1016/j.physa.2017.09.028
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发表时间：
2018-02-01
影响因子：
3.3
通讯作者：
Katz, Yuri
中科院分区：
文献类型：
--
作者：
Gidea, Marian;Katz, Yuri
我们探讨了 2000 年科技崩盘和 2007-2009 年金融危机期间美国四大股市指数每日回报的演变。我们的方法基于拓扑数据分析（TDA）。我们使用持久同源性来检测和量化多维时间序列中出现的拓扑模式。使用滑动窗口，我们提取与时间相关的点云数据集，并将其与拓扑空间相关联。我们检测该空间中出现的瞬态环路，并测量它们的持久性。这被编码在被称为“持久景观”的实值函数中。我们通过 L-P 范数量化持久性景观的时间变化。我们在由各种非线性和非平衡模型生成的多维时间序列上测试这个过程。我们发现，在金融崩溃附近，L-P 范数在初级峰值之前表现出强劲的增长，而初级峰值在崩溃期间上升。值得注意的是，持久性景观的 L-P 范数时间序列的低频平均谱密度表现出在 2000 年 3 月 10 日互联网泡沫崩溃或 2008 年 9 月 15 日雷曼破产之前的 250 个交易日内的强劲上升趋势。我们的研究表明，TDA 提供了一种新型的计量经济分析，它补充了标准统计指标。该方法可用于检测即将发生的市场崩盘的预警信号。我们相信，这种方法可以用于此处介绍的金融时间序列分析之外。 (C) 2017 Elsevier B.V. 保留所有权利。
We explore the evolution of daily returns of four major US stock market indices during the technology crash of 2000, and the financial crisis of 2007-2009. Our methodology is based on topological data analysis (TDA). We use persistence homology to detect and quantify topological patterns that appear in multidimensional time series. Using a sliding window, we extract time-dependent point cloud data sets, to which we associate a topological space. We detect transient loops that appear in this space, and we measure their persistence. This is encoded in real-valued functions referred to as a 'persistence landscapes'. We quantify the temporal changes in persistence landscapes via their L-P-norms. We test this procedure on multidimensional time series generated by various non-linear and non-equilibrium models. We find that, in the vicinity of financial meltdowns, the L-P-norms exhibit strong growth prior to the primary peak, which ascends during a crash. Remarkably, the average spectral density at low frequencies of the time series of L-P-norms of the persistence landscapes demonstrates a strong rising trend for 250 trading days prior to either dotcom crash on 03/10/2000, or to the Lehman bankruptcy on 09/15/2008. Our study suggests that TDA provides a new type of econometric analysis, which complements the standard statistical measures. The method can be used to detect early warning signals of imminent market crashes. We believe that this approach can be used beyond the analysis of financial time series presented here. (C) 2017 Elsevier B.V. All rights reserved.