View source: R/RVineVuongTest.R
RVineVuongTest | R Documentation |
This function performs a Vuong test between two d-dimensional R-vine copula
models as specified by their RVineMatrix()
objects.
RVineVuongTest(data, RVM1, RVM2)
data |
An N x d data matrix (with uniform margins). |
RVM1 , RVM2 |
|
The likelihood-ratio based test proposed by Vuong (1989) can be used for
comparing 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
. We then compute the
standardized sum, \nu
, of the log differences of their pointwise
likelihoods
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\in[0,1],\
i=1,...,N
, i.e.,
\texttt{statistic} := \nu = \frac{\frac{1}{n}\sum_{i=1}^N
m_i}{\sqrt{\sum_{i=1}^N\left(m_i - \bar{m} \right)^2}}.
Vuong
(1989) shows that \nu
is asymptotically standard normal. According to
the null-hypothesis
H_0:
E[m_i] = 0\ \forall i=1,...,N,
we
hence prefer vine model 1 to vine model 2 at level \alpha
if
\nu>\Phi^{-1}\left(1-\frac{\alpha}{2}\right),
where \Phi^{-1}
denotes the inverse of the
standard normal distribution function. If
\nu<-\Phi^{-1}\left(1-\frac{\alpha}{2}\right)
we choose model 2. If, however,
|\nu|\leq\Phi^{-1}\left(1-\frac{\alpha}{2}\right)
, no decision among the models is possible.
Like AIC and BIC, the Vuong 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.
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. |
Jeffrey Dissmann, Eike Brechmann
Vuong, Q. H. (1989). Ratio tests for model selection and non-nested hypotheses. Econometrica 57 (2), 307-333.
RVineClarkeTest()
, RVineAIC()
,
RVineBIC()
# 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))
# 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
vuong <- RVineVuongTest(daxreturns[,1:5], RVM, CVM)
vuong$statistic
vuong$statistic.Schwarz
vuong$p.value
vuong$p.value.Schwarz
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