pacotestRvineSingleCopula {pacotest}

Testing for a Single (j-1)-th Order Partial Copula in a R-Vine Copula

Description

The function can be used to test a single copula in a R-vine copula 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

pacotestRvineSingleCopula(data, RVM, pacotestOptions, tree, copulaNumber)

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.

tree

The tree number (j>=2) of the copula which should be tested to be a (j-1)-th order partial copula.

copulaNumber

The number (1<= copulaNumber <= j-1) of the copula in the normalized RVineMatrix which should be tested to be a (j-1)-th order partial copula.

Value

A list which can, depending on the chosen test, consist of the following elements:

pValue

The p-value of the test.

testStat

The value of the test statistic.

decisionTree

The decision tree used to partition the support Lmabda0 of the conditioning variable W. It is provided as a list consisting of three nodes (CentralNode, LeftNode and RightNode) represented as lists and the variable LeavesForFinalComparison. Each node consists of the Variable used to perform the split, the corresponding Quantile and Threshold.

S

The bootstrapped values of the test statistic (only for the test type VI).

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, pacotestRvineSeq

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:
# For illustrating the functioning of the decision tree,
# grouped scatterplots and a decision tree plot are activated.
pacotestOptions = pacotestset(testType='CCC',
                               groupedScatterplots = TRUE,
                               decisionTreePlot = TRUE)

# Test for a 2-nd order partial copula
# corresponding to the variables BAYN.DE,BMW.DE
# and conditioning set ALV.DE,BAS.DE
tree = 3
copulaNumber = 1

pacotestResultList = pacotestRvineSingleCopula(dataSet, RVM,
                                                pacotestOptions, tree, copulaNumber)