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.
Palabras clave: Topological Data Analysis, Persistence Homology, Financial Time Series
Programado
Pósteres II
7 de junio de 2022 16:50
Hall de la Facultad
