3 research outputs found
Optimal Copula Transport for Clustering Multivariate Time Series
This paper presents a new methodology for clustering multivariate time series
leveraging optimal transport between copulas. Copulas are used to encode both
(i) intra-dependence of a multivariate time series, and (ii) inter-dependence
between two time series. Then, optimal copula transport allows us to define two
distances between multivariate time series: (i) one for measuring
intra-dependence dissimilarity, (ii) another one for measuring inter-dependence
dissimilarity based on a new multivariate dependence coefficient which is
robust to noise, deterministic, and which can target specified dependencies.Comment: Accepted at ICASSP 201
On clustering financial time series: a need for distances between dependent random variables
The following working document summarizes our work on the clustering of
financial time series. It was written for a workshop on information geometry
and its application for image and signal processing. This workshop brought
several experts in pure and applied mathematics together with applied
researchers from medical imaging, radar signal processing and finance. The
authors belong to the latter group. This document was written as a long
introduction to further development of geometric tools in financial
applications such as risk or portfolio analysis. Indeed, risk and portfolio
analysis essentially rely on covariance matrices. Besides that the Gaussian
assumption is known to be inaccurate, covariance matrices are difficult to
estimate from empirical data. To filter noise from the empirical estimate,
Mantegna proposed using hierarchical clustering. In this work, we first show
that this procedure is statistically consistent. Then, we propose to use
clustering with a much broader application than the filtering of empirical
covariance matrices from the estimate correlation coefficients. To be able to
do that, we need to obtain distances between the financial time series that
incorporate all the available information in these cross-dependent random
processes.Comment: Work presented during a workshop on Information Geometry at the
International Centre for Mathematical Sciences, Edinburgh, U
A review of two decades of correlations, hierarchies, networks and clustering in financial markets
We review the state of the art of clustering financial time series and the
study of their correlations alongside other interaction networks. The aim of
this review is to gather in one place the relevant material from different
fields, e.g. machine learning, information geometry, econophysics, statistical
physics, econometrics, behavioral finance. We hope it will help researchers to
use more effectively this alternative modeling of the financial time series.
Decision makers and quantitative researchers may also be able to leverage its
insights. Finally, we also hope that this review will form the basis of an open
toolbox to study correlations, hierarchies, networks and clustering in
financial markets