copula (version 1.1-4)

exchTest: Test of Exchangeability for a Bivariate Copula

Description

Test for assessing the exchangeability of the underlying bivariate copula based on the empirical copula. The test statistics are defined in the first two references. Approximate p-values for the test statistics are obtained by means of a multiplier technique if there are no ties in the component series of the bivariate data, or by means of an appropriate bootstrap otherwise.

Usage

exchTest(x, N = 1000, ties = NA,
         ties.method = eval(formals(rank)$ties.method), m = 0)

Value

An object of class

htest which is a list, some of the components of which are

statistic

value of the test statistic.

p.value

corresponding approximate p-value.

Arguments

x

a data matrix that will be transformed to pseudo-observations.

N

number of multiplier or boostrap iterations to be used to simulate realizations of the test statistic under the null hypothesis.

ties

logical; if FALSE, approximate p-values are computed by means of a multiplier bootstrap; if TRUE, a boostrap adapted to the presence of ties in any of the coordinate samples of x is used; the default value of NA indicates that the presence/absence of ties will be checked for automatically.

ties.method

string specifying how ranks should be computed if there are ties in any of the coordinate samples of x; passed to pobs.

m

if m=0, integration in the Cramér--von Mises statistic is carried out with respect to the empirical copula; if m > 0, integration is carried out with respect to the Lebesgue measure and m specifies the size of the integration grid.

Details

More details are available in the references.

References

Genest, C., G. Nešlehová, J. and Quessy, J.-F. (2012). Tests of symmetry for bivariate copulas. Annals of the Institute of Statistical Mathematics 64, 811--834.

Kojadinovic, I. and Yan, J. (2012). A nonparametric test of exchangeability for extreme-value and left-tail decreasing bivariate copulas. The Scandinavian Journal of Statistics 39:3, 480--496.

Kojadinovic, I. (2017). Some copula inference procedures adapted to the presence of ties. Computational Statistics and Data Analysis 112, 24--41, https://arxiv.org/abs/1609.05519.

See Also

radSymTest, exchEVTest, gofCopula.

Examples

## Data from an exchangeable copulas
exchTest(rCopula(200,  gumbelCopula(3)))
exchTest(rCopula(200, claytonCopula(3)))

## An asymmetric Khoudraji-Clayton copula
kc <- khoudrajiCopula(copula1 = indepCopula(),
                      copula2 = claytonCopula(6),
                      shapes = c(0.4, 0.95))
exchTest(rCopula(200, kc))