Topological Data Analysis, persistence homology and correlation: Applications to multidimensional financial time series.
L. Aromi Leaverton, C. Casacuberta Vergés, D. Farré Gil, Y. A. Katz, J. Vives Santa-Eulalia, J. Vives Santa-Eulalia
Topological data analysis provides a new perspective in Time Series Analysis. In particular, the notion of persistence homology has proven to be fruitful in analyzing multidimensional data clouds.
Given a point cloud generated by a multidimensional distribution we show the relationship between the norm of its persistence landscape and its variance-covariance matrix.
As an application we analyze and distinguish the behavior of daily log-returns of several equity market indices in different periods of crisis such as the technological crash of 2000, the financial crisis of 2007-09 and the exogenous COVID-19 shock of 2020.
This poster is based on:
L. L. Aromi, Y. A. Katz and J. Vives (2021): Topological features of multivariate distributions: dependency on the covariance matrix. Communications in Nonlinear Science and Numerical Simulation 103.
C. Casacuberta, D. Farré and J. Vives (2022): Persistence homology and correlation in multivariate distributions. Work in progress.
Keywords: Topological Data Analysis, Persistence Homology, Financial Time Series
Scheduled
Posters II
June 7, 2022 4:50 PM
Faculty Hall
Other papers in the same session
J. M. Sánchez Santos, A. Berral-Gonzalez, S. Bueno-Fortes, M. Martin-Merino, J. De Las Rivas
A. J. Fernández Ares, N. Rico Castro, D. Romero Molina
J. M. Gutiérrez Expósito, L. A. San José Nieto, B. Abdul-Jalbar Betancor, J. Sicilia Rodríguez
A. F. Roldán López de Hierro, M. M. Rueda García, M. Sánchez Maldonado, C. Roldán
Ú. Torres Parejo, R. Enrique Guillén, M. D. Ruiz Jiménez
J. Navarro, J. Mulero González
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