🍩 Database of Original & Non-Theoretical Uses of Topology

(found 5 matches in 0.001124s)
  1. A Simplified Algorithm for Identifying Abnormal Changes in Dynamic Networks (2022)

    Bouchaib Azamir, Driss Bennis, Bertrand Michel
    Abstract Topological data analysis has recently been applied to the study of dynamic networks. In this context, an algorithm was introduced and helps, among other things, to detect early warning signals of abnormal changes in the dynamic network under study. However, the complexity of this algorithm increases significantly once the database studied grows. In this paper, we propose a simplification of the algorithm without affecting its performance. We give various applications and simulations of the new algorithm on some weighted networks. The obtained results show clearly the efficiency of the introduced approach. Moreover, in some cases, the proposed algorithm makes it possible to highlight local information and sometimes early warning signals of local abnormal changes.
  2. Some Applications of TDA on Financial Markets (2022)

    Miguel Angel Ruiz-Ortiz, José Carlos Gómez-Larrañaga, Jesús Rodríguez-Viorato
    Abstract The Topological Data Analysis (TDA) has had many applications. However, financial markets has been studied slightly through TDA. Here we present a quick review of some recent applications of TDA on financial markets and propose a new turbulence index based on persistent homology -- the fundamental tool for TDA -- that seems to capture critical transitions on financial data, based on our experiment with SP500 data before 2020 stock market crash in February 20, 2020, due to the COVID-19 pandemic. We review applications in the early detection of turbulence periods in financial markets and how TDA can help to get new insights while investing and obtain superior risk-adjusted returns compared with investing strategies using classical turbulence indices as VIX and the Chow's index based on the Mahalanobis distance. Furthermore, we include an introduction to persistent homology so the reader could be able to understand this paper without knowing TDA.
  3. Investigation of Flash Crash via Topological Data Analysis (2020)

    Wonse Kim, Younng-Jin Kim, Gihyun Lee, Woong Kook
    Abstract Topological data analysis has been acknowledged as one of the most successful mathematical data analytic methodologies in various fields including medicine, genetics, and image analysis. In this paper, we explore the potential of this methodology in finance by applying persistence landscape and dynamic time series analysis to analyze an extreme event in the stock market, known as Flash Crash. We will provide results of our empirical investigation to confirm the effectiveness of our new method not only for the characterization of this extreme event but also for its prediction purposes.
  4. A Machine-Learning-Based Early Warning System Boosted by Topological Data Analysis (2019)

    Devraj Basu, Tieqiang Li
    Abstract We propose a novel early warning system for detecting financial market crashes that utilizes the information extracted from the shape of financial market movement. Our system incorporates Topological Data Analysis (TDA), a new set of data analytics techniques specialised in profiling the shape of data, into a more traditional machine learning framework. Incorporating TDA leads to substantial improvements in timely detecting the onset of a sharp market decline. Our framework is both able to generate new features and also unlock more value from existing factors. Our results illustrate the importance of understanding the shape of financial market data and suggest that incorporating TDA into a machine learning framework could be beneficial in a number of financial market settings.
  5. Topological Data Analysis of Financial Time Series: Landscapes of Crashes (2017)

    Marian Gidea, Yuri Katz
    Abstract 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\textasciicircump\$-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\textasciicircump\$-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\textasciicircump\$-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 goes beyond 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.