Optimal Transport vs. Fisher-Rao distance between Copulas for Clustering Multivariate Time Series

TL;DR

This paper compares different distances between copulas, including optimal transport and Fisher-Rao, to improve clustering of multivariate time series, with applications in financial asset analysis.

Contribution

It introduces a methodology for clustering multivariate time series using copula-based distances, comparing their effectiveness and discussing their advantages and disadvantages.

Findings

Optimal transport and Fisher-Rao distances have different advantages for copula comparison.

The methodology improves clustering accuracy in financial asset data.

Reproducible experiments and implementation are provided.

Abstract

We present a methodology for clustering N objects which are described by multivariate time series, i.e. several sequences of real-valued random variables. This clustering methodology leverages copulas which are distributions encoding the dependence structure between several random variables. To take fully into account the dependence information while clustering, we need a distance between copulas. In this work, we compare renowned distances between distributions: the Fisher-Rao geodesic distance, related divergences and optimal transport, and discuss their advantages and disadvantages. Applications of such methodology can be found in the clustering of financial assets. A tutorial, experiments and implementation for reproducible research can be found at www.datagrapple.com/Tech.