gofOutputHybrid {gofCopula}

Output Hybrid gof test

Description

gofOutputHybrid outputs the desired Hybrid tests from previous test results from this package for the specified testing size.

Usage

gofOutputHybrid(result, tests = NULL, nsets = NULL)

Arguments

result

An object of class gofCOP.

tests

Individual tests which should be used in the hybrid test. Submit a vector containing the position of the individual tests as they appear in the object submitted, e.g. c(1,4) for the 1st and 4th tests. If tests is set NULL (default), all possible testing sizes are returned.

nsets

The desired number of tests to be included in each hybrid test. It should be an integer larger than 1 and smaller or equal than the number of tests given in result. If nsets is set NULL (default), all possible testing sizes are calculated.

Details

In most of scenarios for goodness-of-fit tests, including the one for copula models (e.g. Genest et al. (2009)) there exists no single dominant optimal test. Zhang et al. (2015) proposed a hybrid test which performed in their simulation study more desirably compared to the applied single tests.

The p-value is a combination of the single tests in the following way:

p_n^{hybrid} = \min(q \cdot \min{(p_n^{(1)}, \dots, p_n^{(q)})}, 1)

where q is the number of tests and p_n^{(i)} the p-value of the test i. It is ensured that the hybrid test is consistent as long as at least one of the tests is consistent.

The computation of the individual p-values is performed as described in the details of this tests. Note that the derivation differs.

Value

An object of the class gofCOP with the components

method

a character which informs about the performed analysis

copula

the copula tested for

margins

the method used to estimate the margin distribution.

param.margins

the parameters of the estimated margin distributions. Only applicable if the margins were not specified as "ranks" or NULL.

theta

dependence parameters of the copulae

df

the degrees of freedem of the copula. Only applicable for t-copula.

res.tests

a matrix with the p-values and test statistics of the hybrid and the individual tests

References

Zhang, S., Okhrin, O., Zhou, Q., and Song, P.. Goodness-of-fit Test For Specification of Semiparametric Copula Dependence Models. Journal of Econometrics, 193, 2016, pp. 215-233 doi: 10.1016/j.jeconom.2016.02.017

Examples

data(IndexReturns2D)

res1 = gof(IndexReturns2D, priority = "tests", copula = "normal", 
           tests = c("gofKendallCvM", "gofRosenblattSnC", "gofKendallKS"), 
           M = 5)
gofOutputHybrid(res1, tests = 1, nsets = 2)
# mind the difference to the regular output
res1