VineCopula (version 2.6.1)

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)

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.

Arguments

data

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

RVM1, RVM2

RVineMatrix() objects of models 1 and 2.

Author

Jeffrey Dissmann, Eike Brechmann

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 ${\hat{\mathit{\theta }}}_1$ and ${\hat{\mathit{\theta }}}_2$. The null hypothesis of statistical indistinguishability of the two models is $$H_0:P(m_i>0)=0.5\mathrm{\forall }i=1,..,N,$$ where $m_i:=\log \left[\frac{c_1({\mathit{u}}_i|{\hat{\mathit{\theta }}}_1)}{c_2({\mathit{u}}_i|{\hat{\mathit{\theta }}}_2)}\right]$ for observations ${\mathit{u}}_i,i=1,...,N$.

Since under statistical equivalence of the two models the log likelihood ratios of the single observations are uniformly distributed around zero and in expectation $50\mathrm{\%}$ of the log likelihood ratios greater than zero, the test statistic $$\mathtt{\text{statistic}}:=B=\sum _{i=1}^N{\mathbf{1}}_{(0,\mathrm{\infty })}(m_i),$$ 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

# vine structure selection time-consuming (~ 20 sec)

# load data set
data(daxreturns)
daxreturns <- daxreturns[1:200, ]

# select the R-vine structure, families and parameters
RVM <- RVineStructureSelect(daxreturns[,1:5], c(1:6))
RVM$Matrix
RVM$par
RVM$par2

# select the C-vine structure, families and parameters
CVM <- RVineStructureSelect(daxreturns[,1:5], c(1:6), type = "CVine")
CVM$Matrix
CVM$par
CVM$par2

# 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