Tail-weighted measures of dependence

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Tail-weighted measures of dependence

TitleTail-weighted measures of dependence
Publication TypeJournal Article
Year of Publication2015
AuthorsKrupskii, P, Joe, H
JournalJournal of Applied Statistics
Volume42
Pagination614-629
Date PublishedMAR 4
Type of ArticleArticle
ISSN0266-4763
Keywords62H20, Copula, Dependence measure, factor model, intermediate tail dependence, Tail asymmetry, Tail dependence
AbstractMultivariate copula models are commonly used in place of Gaussian dependence models when plots of the data suggest tail dependence and tail asymmetry. In these cases, it is useful to have simple statistics to summarize the strength of dependence in different joint tails. Measures of monotone association such as Kendall's tau and Spearman's rho are insufficient to distinguish commonly used parametric bivariate families with different tail properties. We propose lower and upper tail-weighted bivariate measures of dependence as additional scalar measures to distinguish bivariate copulas with roughly the same overall monotone dependence. These measures allow the efficient estimation of strength of dependence in the joint tails and can be used as a guide for selection of bivariate linking copulas in vine and factor models as well as for assessing the adequacy of fit of multivariate copula models. We apply the tail-weighted measures of dependence to a financial data set and show that the measures better discriminate models with different tail properties compared to commonly used risk measures - the portfolio value-at-risk and conditional tail expectation.
DOI10.1080/02664763.2014.980787