# SeqTestOnSimplified (VineCopulaObject)

Sequentially testing the simplified assumption for vine copulas

## 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.
```