SeqTestOnSimplified (VineCopulaObject)

Sequentially testing the simplified assumption for vine copulas

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Purpose

The function can be used to sequentially test the simplifying assumption for vine copulas. The procedure heavily relies on a stochastic representation of the simplifying assumption stated in Spanhel and Kurz (2014). The stochastic representation allows to test the simplifying assumption by using tests on vectorial independencies. Note, that the performed tests are always based on the assumption that one is able to observe (pseudo-)observations from the conditional copulas that should be tested. Therefore, for interpreting the test results for a specific tree of the vine copula one needs to assume that the lower trees (including the assumption of unconditional copulas) are correctly specified.

Usage

    Testing the simplifying assumption sequentially
     [pVals,TestStats,BootTestStats] = SeqTestOnSimplified(VineCopulaObject,data,N)
    Testing the simplifying assumption sequentially as
    goodness-of-fit test (i.e., without reestimating the
    whole vine copula for each tree)
     [pVals,TestStats,BootTestStats] = SeqTestOnSimplified(VineCopulaObject,data,N,true)

Inputs

    VineCopulaObject      = An object from the class
                            VineCopula.
    data                  = A (n x d) dimensional vector
                            of values lying in [0,1] (the
                            observations).
    N                     = The number of boostrap
                            replications for the
                            multiplier bootstrap in the
                            vectorial independence test.
    GoF                   = A logical, which is by default
                            false. Then, before the tests
                            on vectorial independence are
                            applied in each tree, the
                            whole vine copula model is
                            reestimated up to this tree
                            and then the tests are
                            performed. Otherwise, i.e., if
                            it is applied as a goodness-
                            of-fit test, the joint
                            estimates given as inputs
                            through the VineCopula object
                            are used to obtain the
                            (pseudo-)observations in each
                            tree (without re-estimation).

Outputs

    pVal                  = A vector of p-values of the
                            vectorial independence tests. 
                            Every entry corresponds to one
                            specific copula being part
                            of the whole vine copula.
    TestStat              = A vector of realized values
                            for the test statistics.
                            of the whole vine copula.
    BootTestStats         = A matrix of realized values
                            for the bootstrapped test
                            statistics.