Comment partitionner automatiquement des marches al\'eatoires ? Avec application \`a la finance quantitative

TL;DR

This paper introduces a non-parametric method for clustering Markov processes, particularly applied to financial time series, by transforming data into a dependency-marginal distribution factorized representation and defining a tunable metric.

Contribution

It proposes a novel non-parametric pre-processing step and a dependency-sensitive metric for clustering Markov processes, with practical application to financial data.

Findings

Effective clustering of financial time series demonstrated

Method implemented and available online

Parameter tuning influences clustering results

Abstract

We present in this paper a novel non-parametric approach useful for clustering Markov processes. We introduce a pre-processing step consisting in mapping multivariate independent and identically distributed samples from random variables to a generic non-parametric representation which factorizes dependency and marginal distribution apart without losing any. An associated metric is defined where the balance between random variables dependency and distribution information is controlled by a single parameter. This mixing parameter can be learned or played with by a practitioner, such use is illustrated on the case of clustering financial time series. Experiments, implementation and results obtained on public financial time series are online on a web portal \url{http://www.datagrapple.com}.