Large-sample tests of extreme-value dependence for multivariate copulas

Ivan Kojadinovic A · Johan Segers · Jun Yan

48 citations0/0 files storedCanadian Journal of Statistics

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Financial Risk and Volatility Modeling Statistical Distribution Estimation and Applications Probability and Risk Models

Abstract

Starting from the characterization of extreme-value copulas based on max-stability, large-sample tests of extreme-value dependence for multivariate copulas are studied. The two key ingredients of the proposed tests are the empirical copula of the data and a multiplier technique for obtaining approximate p-values for the derived statistics. The asymptotic validity of the multiplier approach is established, and the finite-sample performance of a large number of candidate test statistics is studied through extensive Monte Carlo experiments for data sets of dimension two to five. In the bivariate case, the rejection rates of the best versions of the tests are compared with those of the test of Ghoudi et al. (1998) recently revisited by Ben Ghorbal et al. (2009). The proposed procedures are illustrated on bivariate financial data and trivariate geological data. The Canadian Journal of Statistics 39: 703–720; 2011. © 2011 Statistical Society of Canada

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References

1999An Introduction to Copulas 1990The Asymptotic Theory of Extreme Order Statistics 1998Understanding Relationships Using Copulas 2011Quantitative Risk Management 1988Bivariate Extreme Value Theory: Models and Estimation 2014Extremes in Nature: An Approach Using Copulas 2004Weak convergence of empirical copula processes 2010Modeling Multivariate Distributions with Continuous Margins Using the copula R Package

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2010Nonparametric rank-based tests of bivariate extreme-value dependence 2013An Overview of the Goodness-of-Fit Test Problem for Copulas 2015A class of multivariate copulas based on products of bivariate copulas 2021Nonparametric sequential change-point detection for multivariate time series based on empirical distribution functions

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