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http://hdl.handle.net/2445/193830
Title: | Topological features of multivariate distributions: Dependency on the covariance matrix |
Author: | Aromi, Lloyd L. Katz, Yuri A. Vives i Santa Eulàlia, Josep, 1963- |
Keywords: | Processos estocàstics Estadística Grups topològics Homologia Stochastic processes Statistics Topological groups Homology |
Issue Date: | 14-Aug-2021 |
Publisher: | Elsevier B.V. |
Abstract: | Topological data analysis provides a new perspective on many problems in the domain of complex systems. Here, we establish the dependency of mean values of functional $p$ norms of 'persistence landscapes' on a uniform scaling of the underlying multivariate distribution. Furthermore, we demonstrate that average values of $p$-norms are decreasing, when the covariance in a system is increasing. To illustrate the complex dependency of these topological features on changes in the variance-covariance matrix, we conduct numerical experiments utilizing bi-variate distributions with known statistical properties. Our results help to explain the puzzling behavior of $p$-norms derived from daily log-returns of major equity indices on European and US markets at the inception phase of the global financial meltdown caused by the COVID-19 pandemic. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1016/j.cnsns.2021.105996 |
It is part of: | Communications In Nonlinear Science And Numerical Simulation, 2021, vol. 103, num. 105996 |
URI: | http://hdl.handle.net/2445/193830 |
Related resource: | https://doi.org/10.1016/j.cnsns.2021.105996 |
ISSN: | 1007-5704 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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