Tests of symmetry for bivariate copulas

Abstract

Tests are proposed for the hypothesis that the underlying copula of a continuous random pair is symmetric. The procedures are based on Cramér-von Mises and Kolmogorov-Smirnov functionals of a rank-based empirical process whose largesample behaviour is obtained. The asymptotic validity of a re-sampling method to compute P values is also established. The technical arguments supporting the use of a Chi-squared test due to Jasson are also presented. A power study suggests that the proposed tests are more powerful than Jasson's procedure under many scenarios of copula asymmetry. The methods are illustrated on a nutrient data set.

Evolution of Coupled Lives' Dependency Across Generations and Pricing Impact

“…which, according to Genest et al (2012) was found to be superior to alternative tests proposed. For our data set, the p-values are 0.247 (OG) and 0.162 (YG).…”

“…Since for both generations the comparison 3P-vs-2P is either problematic or gives contradictory answers, and recalling that 2P copulas display symmetry while 3P ones do not, we have conducted a generic test on symmetry of bivariate copulas, due to Genest et al (2012). Unlike the Chen and Fan test, this test does not require a priori speci…cation of the parametric copula, but is based on a consistent nonparametric estimate of the copula:…”

Goodness-of-Fit Tests for Multivariate Copula-Based Time Series Models

“…It has been proposed in Scaillet (2005) and Rémillard and Scaillet (2009) for i.i.d. data sets, and has been applied to different testing issues in Genest et al (2011);Bücher et al (2011Bücher et al ( , 2012, among others. The procedure has been generalized to the alpha-mixing case in Bücher and Ruppert (2013) with several further improvements in Bücher and Kojadinovic (2013).…”

Testing Asymmetry in Dependence with Copula-Coskewness

“…departures from symmetry, which was proposed by Genest et al (2011) with a recent application in Siburg et al (2016).…”

“…Note that the result does not require any smoothness assumptions on the copula at all. This is in contrast to, for instance, the test for symmetry of Genest et al (2011) which relys on the assumption of existing continuous first order partial derivatives of the copula C. The formal test that we are going to derive below can hence be used under far broader conditions than the test of Genest et al (2011).…”