pacotestRvineSeq {pacotest}

Sequentially Testing the Simplifying Assumption for R-Vine Copulas

Description

The function can be used to test the simplifying assumption for R-vine copulas in a sequential manner. Each pair-copula from the second tree on is tested to be a (j-1)-th order partial copula. To apply the function one needs to provide the data and a specified/estimated R-vine copula model in form of a RVineMatrix from the VineCopula-package. Additionally, a pacotest options list, which can be generated with the pacotestset function, needs to be provided.

Usage

pacotestRvineSeq(data, RVM, pacotestOptions,
  level = 0.05, illustration = 2, stopIfRejected = TRUE)

Arguments

data

A (n x d) matrix (or data frame) of [0,1] data (i.e. uniform margins).

RVM

An RVineMatrix object (VineCopula-package) which includes the structure, the pair-copula families and parameters of an R-vine copula.

pacotestOptions

A options list generated by the pacotestset function or the test type as string, i.e., CCC or VI.

level

The level of the test.

illustration

Either 1 or 2. If illustration = 1, the p-value for each test for a (j-1)-th order partial copula is displayed. If illustration = 2, a progress information is displayed for each tree. It consists of the individual test level and the number of H0 rejections.

stopIfRejected

A logical variable indicating whether the sequential test procedure should be stopped in the first tree where an H0 for one of the conditional copulas is rejected.

Value

A list consisting of the following elements:

pacotestResultLists

A matrix in the same structure like the Matrix, family, par, etc. entries in the RVineMatrix object from the VineCopula-package. Each entry of the matrix is a list containing the test result from a test for a (j-1)-th order partial copula obtained from a call to pacotest. Depending on the chosen test, it could consist of different elements. A documentation of the pacotestResultLists can be found in the documentation of pacotest.

pValues

A matrix in the same structure like the Matrix, family, par, etc. entries in the RVineMatrix object from the VineCopula-package. Each entry of the matrix is a p-value corresponding to the test result from a test for a (j-1)-th order partial copula.

testResultSummary

A data.frame summarizing the test results. The first column, Tree, is the tree number. The second column, NumbOfRejections, is the number of of rejections in the corresponding tree. The third column, IndividualTestLevel, is the level at which each individual test has been performed. The fourth column, Interpretation, provides an interpretation of the test result.

Author(s)

Malte S. Kurz

References

Kurz, M. S. and F. Spanhel (2022), "Testing the simplifying assumption in high-dimensional vine copulas", Electronic Journal of Statistics 16 (2), pp. 5226-5276.

Spanhel, F. and M. S. Kurz (2019), "Simplified vine copula models: Approximations based on the simplifying assumption", Electronic Journal of Statistics 13 (1), pp. 1254-1291.

See Also

pacotest-package, pacotest, pacotestset, pacotestRvineSingleCopula

Examples

# Sample data and R-vine copula selection are taken
# from the documentation of RVineStructureSelect
# of the VineCopula package.

# Obtain sample data
data(daxreturns, package ="VineCopula")
dataSet = daxreturns[1:750,1:4]

# Specify an R-vine copula model
# (can be obtained by calling: RVM = VineCopula::RVineStructureSelect(dataSet))
vineStructure = matrix(c(3,4,1,2,0,2,4,1,0,0,1,4,0,0,0,4),4,4)
families = matrix(c(0,5,2,2,0,0,2,14,0,0,0,14,0,0,0,0),4,4)
par = matrix(c(0,0.8230664,0.1933472,0.6275062,
             0,0,0.2350109,1.6619945,
             0,0,0,1.599363,
             0,0,0,0),4,4)
par2 = matrix(c(0,0,11.757700,4.547847,
             0,0,17.15717,0,
             0,0,0,0,0,0,0,0),4,4)
RVM = VineCopula::RVineMatrix(vineStructure, families, par, par2)


# Specify a pacotestOptions list:
pacotestOptions = pacotestset('CCC')

# Test for the simplifying assumption.
pacotestResultList = pacotestRvineSeq(dataSet, RVM,
                                      pacotestOptions)