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

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 θ_1 and θ_2. The null hypothesis of statistical indistinguishability of the two models is

H_0: P(m_i > 0) = 0.5 forall i=1,..,N,

H_0: P(m_i > 0) = 0.5 forall i=1,..,N,

where m_i:=log[ c_1(u_i|θ_1) / c_2(u_i|θ_2) ] for observations 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

statistic := B = ∑_{i=1}^N 1_{(0,∞)}(m_i),

statistic := B = ∑_{i=1}^N 1_{(0,∞)}(m_i),

where 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=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.

Value

Author(s)

Jeffrey Dissmann, Eike Brechmann

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)


# 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

Results