Sequentially testing the simplified assumption for vine copulas
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.
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)
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).
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.