RVineClarkeTest {VineCopula} | R Documentation |
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 |
|
Details
The test proposed by Clarke (2007) allows to compare non-nested models. For
this let and
be two competing vine copulas in terms of
their densities and with estimated parameter sets
and
. The null hypothesis of
statistical indistinguishability of the two models is
where
for observations
.
Since under statistical equivalence of the two models the log likelihood
ratios of the single observations are uniformly distributed around zero and
in expectation of the log likelihood ratios greater than zero,
the test statistic
where is the indicator function,
is distributed Binomial with parameters
and
, and
critical values can easily be obtained. Model 1 is interpreted as
statistically equivalent to model 2 if
is not significantly
different from the expected value
.
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
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. |
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