Afrika Statistika

Nonparametric confidence intervals for tail dependence based on copulas

Cheikh Tidiane SECK, Ba DIAM, and Gane Samb LO

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Abstract

We propose nonparametric asymptotic confidence intervals for the upper and lower tail dependence coefficients. These latter are obtained from confidence bands established for the copula function itself and based upon three kernel-type estimators. We show the performance of these confidence intervals through a simulation study. We also apply these results to financial data stemming from the CAC 40 stock index which reveals the existence of extreme dependence between larger values of the opening and closing prices for this index during the considered period.

Résumé

Ce papier présente des intervalles de confiance asymptotiques pour les coefficients de dépendance de queue inférieure et supérieure. Ces derniers sont obtenus de façon nonparamétrique à partir de bandes de confiance presque sûres obtenues pour la fonction copule elle méme et basées sur des estimateurs à noyau. Nous montrons ensuite la performance de ces intervalles de confiance à travers une étude de simulation. Une application de ces résultats sur des données financières issues de l'indice boursier CAC 40 révèlent une dépendance extréme entre les valeurs d'ouverture et de fermeture de cet indice durant la période étudiée.

Article information

Source
Afr. Stat., Volume 11, Number 2 (2016), 1023-1039.

Dates
First available in Project Euclid: 20 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.as/1484881313

Digital Object Identifier
doi:10.16929/as/2016.1023.90

Mathematical Reviews number (MathSciNet)
MR3599805

Zentralblatt MATH identifier
1358.62049

Subjects
Primary: 62G20: Asymptotic properties 62H20: Measures of association (correlation, canonical correlation, etc.) 62P05: Applications to actuarial sciences and financial mathematics

Keywords
Tail dependence coefficient Confidence intervals Kernel estimators Copula function

Citation

SECK, Cheikh Tidiane; DIAM, Ba; LO, Gane Samb. Nonparametric confidence intervals for tail dependence based on copulas. Afr. Stat. 11 (2016), no. 2, 1023--1039. doi:10.16929/as/2016.1023.90. https://projecteuclid.org/euclid.as/1484881313


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