Exploring and measuring non-linear correlations: Copulas, Lightspeed Transportation and Clustering
We propose a methodology to explore and measure the pairwise correlations that exist between variables in a dataset. The methodology leverages copulas for encoding dependence between two variables, state-of-the-art optimal transport for providing a relevant geometry to the copulas, and clustering for summarizing the main dependence patterns found between the variables. Some of the clusters centers can be used to parameterize a novel dependence coefficient which can target or forget specific dependence patterns. Finally, we illustrate and benchmark the methodology on several datasets. Code and numerical experiments are available online for reproducible research.
Code (1)
Tasks
ClusteringSimilar Papers 제목 키워드 기반
Impact of non-stationarity on estimating and modeling empirical copulas of daily stock returns
All too often measuring statistical dependencies between financial time series is reduced to a linear correlation coefficient. However this may not capture all facets of reality. We study empirical dependencies of daily …
Time SeriesTime Series AnalysisOptimal 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) int…
ClusteringClustering Multivariate Time SeriesTime SeriesTime Series AnalysisExploiting Hierarchical Dependence Structures for Unsupervised Rank Fusion in Information Retrieval
The goal of rank fusion in information retrieval (IR) is to deliver a single output list from multiple search results. Improving performance by combining the outputs of various IR systems is a challenging task. A central…
Information RetrievalRetrievalDependence structure of market states
We study the dependence structure of market states by estimating empirical pairwise copulas of daily stock returns. We consider both original returns, which exhibit time-varying trends and volatilities, as well as locall…
Vector copulas
This paper introduces vector copulas associated with multivariate distributions with given multivariate marginals, based on the theory of measure transportation, and establishes a vector version of Sklar's theorem. The l…