copula (version 0.999-7)

gofEVCopula: Goodness-of-fit Tests for Bivariate Extreme-Value Copulas

Description

Goodness-of-fit tests for extreme-value copulas based on the empirical process comparing one of the two nonparameteric rank-based estimator of the Pickands dependence function studied in Genest and Segers (2009) with a parametric estimate of the Pickands dependence function derived under the null hypothesis. The test statistic is the Cramer-von Mises functional Sn defined in Equation (5) of Genest, Kojadinovic, G. Nešlehová{Neslehova}, and Yan (2010). Approximate p-values for the test statistic are obtained using a parametric bootstrap.

Usage

gofEVCopula(copula, x, N = 1000, method = "mpl",
            estimator = "CFG", m = 1000, verbose = TRUE,
            print.every = NULL, optim.method = "Nelder-Mead")

Arguments

copula

object of class "evCopula" representing the hypothesized extreme-value copula family.

x

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

N

number of bootstrap samples to be used to simulate realizations of the test statistic under the null hypothesis.

method

estimation method to be used to estimate the dependence parameter(s); can be either "mpl" (maximum pseudo-likelihood), "itau" (inversion of Kendall's tau) or "irho" (inversion of Spearman's rho).

estimator

specifies which nonparametric rank-based estimator of the unknown Pickands dependence function to use; can be either "CFG" (Caperaa-Fougeres-Genest) or "Pickands".

m

number of points of the uniform grid on [0,1] used to compute the test statistic numerically.

print.every

is deprecated in favor of verbose.

verbose

a logical specifying if progress of the bootstrap should be displayed via txtProgressBar.

optim.method

the method for "optim".

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.
• parameter
  estimates of the parameters for the hypothesized copula family.

Details

More details can be found in the second reference.

References

Genest, C. and Segers, J. (2009). Rank-based inference for bivariate extreme-value copulas. Annals of Statistics 37, 2990--3022.

Genest, C. Kojadinovic, I., G. Nešlehová{Neslehova}, J., and Yan, J. (2011). A goodness-of-fit test for bivariate extreme-value copulas. Bernoulli 17(1), 253--275.

See Also

evCopula, evTestC, evTestA, evTestK, gofCopula, An.

Examples

x <- rCopula(100, claytonCopula(3))

## Does the Gumbel family seem to be a good choice?
gofEVCopula(gumbelCopula(1), x)

## The same with different estimation methods
gofEVCopula(gumbelCopula(1), x, method="itau")
gofEVCopula(gumbelCopula(1), x, method="irho")

## The same with different extreme-value copulas
gofEVCopula(galambosCopula(1), x)
gofEVCopula(galambosCopula(1), x, method="itau")
gofEVCopula(galambosCopula(1), x, method="irho")

gofEVCopula(huslerReissCopula(1), x)
gofEVCopula(huslerReissCopula(1), x, method="itau")
gofEVCopula(huslerReissCopula(1), x, method="irho")

gofEVCopula(tevCopula(0, df.fixed=TRUE), x)
gofEVCopula(tevCopula(0, df.fixed=TRUE), x, method="itau")
gofEVCopula(tevCopula(0, df.fixed=TRUE), x, method="irho")