Efficient and Accurate Evaluation Methods for Concordance Measures via Functional Tensor Characterizations of Copulas

Antonio Dalessandro, Gareth W. Peters

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Abstract

There is now an increasingly large number of proposed concordance measures available to capture, measure and quantify different notions of dependence in stochastic processes. However, evaluation of concordance measures to quantify such types of dependence for different copula models can be challenging. In this work, we propose a class of new methods that involves a highly accurate and computationally efficient procedure to evaluate concordance measures for a given copula, applicable even when sampling from the copula is not easily achieved. In addition, this then allows us to reconstruct maps of concordance measures locally in all regions of the state space for any range of copula parameters. We believe this technique will be a valuable tool for practitioners to understand better the behaviour of copula models and associated concordance measures expressed in terms of these copula models.

Original languageEnglish
Pages (from-to)1-36
Number of pages36
JournalMethodology and Computing in Applied Probability
Early online date5 Dec 2019
DOIs
Publication statusE-pub ahead of print - 5 Dec 2019

Keywords

  • Concordance measures
  • Copula functions
  • Copula infinitesimal generators
  • Martingale problem
  • Multidimensional semimartingales decomposition approximations
  • Semimartingales decomposition
  • Tensor algebra

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)

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