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

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