Amb motiu del tancament d'estiu, la validació de documents es reprendrà a partir del 28 d'agost de 2026. Disculpeu les molèsties.
Con motivo del cierre de verano, la validación de documentos se reanudará a partir del 28 de agosto de 2026. Disculpad las molestias
Due to the summer closure, document validation will resume starting August 28, 2026. We apologize for any inconvenience.

Files

720837.pdf (540.15 KB)

Document type

Article

Version

Accepted version

Publication date

2021-08-14

Publication license

cc-by-nc-nd (c) Elsevier B.V., 2021
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/193830

Topological features of multivariate distributions: Dependency on the covariance matrix

Journal Title

Authors

Director/Tutor

Journal ISSN

Volume Title

Related resource

https://doi.org/10.1016/j.cnsns.2021.105996

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.

Subject

Processos estocàstics, Estadística, Grups topològics, Homologia

Subject (English)

Stochastic processes, Statistics, Topological groups, Homology

Citation

Collections

Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

AROMI, Lloyd L., KATZ, Yuri A. and VIVES I SANTA EULÀLIA, Josep. Topological features of multivariate distributions: Dependency on the covariance matrix. Communications In Nonlinear Science And Numerical Simulation. 2021. Vol. 103, num. 105996. ISSN 1007-5704. [consulted: 15 of August of 2026]. Available at: https://hdl.handle.net/2445/193830

Export metadata

JSON - METS

Share record