论文标题
基于持续的基于 - 基因的湍流指数和TDA在金融市场上的某些应用
A persistent-homology-based turbulence index & some applications of TDA on financial markets
论文作者
论文摘要
拓扑数据分析（TDA）是一种现代的数据分析方法，重点是数据的拓扑特征；近年来，它已被广泛研究，并广泛用于生物学，物理和许多其他领域。但是，通过TDA略微研究了金融市场。在这里，我们对TDA在金融市场上的一些最新应用进行了快速审查，包括在金融市场中湍流期间早期发现的应用以及TDA如何在投资时获得新的见解。此外，我们提出了一个基于持续的同源性（TDA的基本工具）的新湍流指数，该指数似乎可以捕获财务数据中的关键过渡；我们通过不同的财务时间序列（S＆P500，Russel 2000，S＆P/BMV IPC和Nikkei 225）和崩溃事件（黑色星期一崩溃，Dot-Com崩溃，2007-08 Crash和Covid-19 Crash）测试了指数。此外，我们还包括持久同源性的介绍，以便读者可以理解本文而不知道TDA。
Topological Data Analysis (TDA) is a modern approach to Data Analysis focusing on the topological features of data; it has been widely studied in recent years and used extensively in Biology, Physics, and many other areas. However, financial markets have been studied slightly through TDA. Here we present a quick review of some recent applications of TDA on financial markets, including applications in the early detection of turbulence periods in financial markets and how TDA can help to get new insights while investing. Also, we propose a new turbulence index based on persistent homology -- the fundamental tool for TDA -- that seems to capture critical transitions in financial data; we tested our index with different financial time series (S&P500, Russel 2000, S&P/BMV IPC and Nikkei 225) and crash events (Black Monday crash, dot-com crash, 2007-08 crash and COVID-19 crash). Furthermore, we include an introduction to persistent homology so the reader can understand this paper without knowing TDA.
