VineCopula (version 1.3)

RVineClarkeTest: Clarke test comparing two R-vine copula models

Description

This function performs a Clarke test between two d-dimensional R-vine copula models as specified by their RVineMatrix objects.

Usage

RVineClarkeTest(data, RVM1, RVM2)

Arguments

data

An N x d data matrix (with uniform margins).

RVM1, RVM2

RVineMatrix objects of models 1 and 2.

Value

• statistic, statistic.Akaike, statistic.Schwarz
  Test statistics without correction, with Akaike correction and with Schwarz correction.
• p.value, p.value.Akaike, p.value.Schwarz
  P-values of tests without correction, with Akaike correction and with Schwarz correction.

Details

The test proposed by Clarke (2007) allows to compare non-nested models. For this let $c_1$ and $c_2$ be two competing vine copulas in terms of their densities and with estimated parameter sets $\hat{\boldsymbol{\theta}}_1$ and $\hat{\boldsymbol{\theta}}_2$. The null hypothesis of statistical indistinguishability of the two models is $$H_0: P(m_i > 0) = 0.5\ \forall i=1,..,N,$$ where $m_i:=\log\left[\frac{c_1(\boldsymbol{u}_i|\hat{\boldsymbol{\theta}}_1)}{c_2(\boldsymbol{u}_i|\hat{\boldsymbol{\theta}}_2)}\right]$ for observations $\boldsymbol{u}_i,\ i=1,...,N$. Since under statistical equivalence of the two models the log likelihood ratios of the single observations are uniformly distributed around zero and in expectation $50%$ of the log likelihood ratios greater than zero, the tets statistic $$\texttt{statistic} := B = \sum_{i=1}^N \mathbf{1}_{(0,\infty)}(m_i),$$ where $\mathbf{1}$ is the indicator function, is distributed Binomial with parameters $N$ and $p=0.5$, and critical values can easily be obtained. Model 1 is interpreted as statistically equivalent to model 2 if $B$ is not significantly different from the expected value $Np = \frac{N}{2}$. Like AIC and BIC, the Clarke test statistic may be corrected for the number of parameters used in the models. There are two possible corrections; the Akaike and the Schwarz corrections, which correspond to the penalty terms in the AIC and the BIC, respectively.

References

Clarke, K. A. (2007). A Simple Distribution-Free Test for Nonnested Model Selection. Political Analysis, 15, 347-363.

See Also

RVineVuongTest, RVineAIC, RVineBIC

Examples

# load data set
data(daxreturns)

# select the R-vine structure, families and parameters
RVM = RVineStructureSelect(daxreturns[,1:5],c(1:6))

# select the C-vine structure, families and parameters
CVM = RVineStructureSelect(daxreturns[,1:5],c(1:6),type="CVine")

# compare the two models based on the data
clarke = RVineClarkeTest(daxreturns[,1:5],RVM,CVM)
clarke$statistic
clarke$statistic.Schwarz
clarke$p.value
clarke$p.value.Schwarz