CDVineAIC-BIC {CDVine} | R Documentation |
These functions calculate the Akaike and Bayesian Information criteria of d-dimensional C- and D-vine copula models for a given copula data set.
CDVineAIC(data, family, par, par2=rep(0,dim(data)[2]*(dim(data)[2]-1)/2), type) CDVineBIC(data, family, par, par2=rep(0,dim(data)[2]*(dim(data)[2]-1)/2), type)
data |
An N x d data matrix (with uniform margins). |
family |
A d*(d-1)/2 integer vector of C-/D-vine pair-copula families with values |
par |
A d*(d-1)/2 vector of pair-copula parameters. |
par2 |
A d*(d-1)/2 vector of second parameters for two parameter pair-copula families
(default: |
type |
Type of the vine model: |
If k denotes the number of parameters of a C-vine copula model with log-likelihood l_{CVine} and parameter set θ, then the Akaike Information Criterion (AIC) by Akaike (1973) is defined as
AIC := -2 l_{CVine}(θ|u) + 2 k,
for observations u=(u'_1,...u'_N).
Similarly, the Bayesian Information Criterion (BIC) by Schwarz (1978) is given by
BIC := -2 l_{CVine}(θ|u) + log(N) k.
The AIC and BIC expressions for D-vine copula models are defined accordingly.
AIC, BIC |
The computed AIC or BIC value, respectively. |
pair.AIC, pair.BIC |
An array of individual contributions to the AIC or BIC value
for each pair-copula, respectively. Note: |
Eike Brechmann
Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N. Petrov and F. Csaki (Eds.), Proceedings of the Second International Symposium on Information Theory Budapest, Akademiai Kiado, pp. 267-281.
Schwarz, G. E. (1978). Estimating the dimension of a model. Annals of Statistics 6 (2), 461-464.
CDVineLogLik
, CDVineVuongTest
, CDVineClarkeTest
## Example 1: 3-dimensional D-vine model with Gaussian pair-copulas data(worldindices) Data = as.matrix(worldindices)[,1:3] fam1 = c(1,1,1) par1 = c(0.2,0.3,0.4) # calculate AIC and BIC CDVineAIC(Data,fam1,par1,type=2) CDVineBIC(Data,fam1,par1,type=2) ## Example 2: 6-dimensional C-vine model with Student t pair-copulas ## with 5 degrees of freedom data(worldindices) Data = as.matrix(worldindices) dd = dim(Data)[2]*(dim(Data)[2]-1)/2 fam2 = rep(2,dd) par2 = rep(0.5,dd) nu2 = rep(5,dd) # calculate AIC and BIC CDVineAIC(Data,fam2,par2,nu2,type=1) CDVineBIC(Data,fam2,par2,nu2,type=1) ## Example 3: 4-dimensional C-vine model with mixed pair-copulas fam3 = c(5,1,3,14,3,2) par3 = c(0.9,0.3,0.2,1.1,0.2,0.7) nu3 = c(0,0,0,0,0,7) # calculate AIC and BIC CDVineAIC(Data[,1:4],fam3,par3,nu3,type=1) CDVineBIC(Data[,1:4],fam3,par3,nu3,type=1)