CDVineAICBIC: AIC and BIC of C- and D-vine copula models
In CDVine: Statistical Inference of C- And D-Vine Copulas

Description Usage Arguments Details Value Author(s) References See Also Examples

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 `0` = independence copula `1` = Gaussian copula `2` = Student t copula (t-copula) `3` = Clayton copula `4` = Gumbel copula `5` = Frank copula `6` = Joe copula `7` = BB1 copula `8` = BB6 copula `9` = BB7 copula `10` = BB8 copula `13` = rotated Clayton copula (180 degrees; “survival Clayton”) `14` = rotated Gumbel copula (180 degrees; “survival Gumbel”) `16` = rotated Joe copula (180 degrees; “survival Joe”) `17` = rotated BB1 copula (180 degrees; “survival BB1”) `18` = rotated BB6 copula (180 degrees; “survival BB6”) `19` = rotated BB7 copula (180 degrees; “survival BB7”) `20` = rotated BB8 copula (180 degrees; “survival BB8”) `23` = rotated Clayton copula (90 degrees) `24` = rotated Gumbel copula (90 degrees) `26` = rotated Joe copula (90 degrees) `27` = rotated BB1 copula (90 degrees) `28` = rotated BB6 copula (90 degrees) `29` = rotated BB7 copula (90 degrees) `30` = rotated BB8 copula (90 degrees) `33` = rotated Clayton copula (270 degrees) `34` = rotated Gumbel copula (270 degrees) `36` = rotated Joe copula (270 degrees) `37` = rotated BB1 copula (270 degrees) `38` = rotated BB6 copula (270 degrees) `39` = rotated BB7 copula (270 degrees) `40` = rotated BB8 copula (270 degrees)
`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: `par2 = rep(0,dim(data)[2](dim(data)[2]-1)/2)`).
`type`	Type of the vine model: `1` or `"CVine"` = C-vine `2` or `"DVine"` = D-vine

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: `AIC = sum(pair.AIC)` and similarly `BIC = sum(pair.BIC)`.

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)

The CDVine package is no longer developed actively.
Please consider using the more general VineCopula package
(see https://CRAN.R-project.org/package=VineCopula),
which extends and improves the functionality of CDVine.

$AIC
[1] -18.36512

$pair.AIC
[1] -14.83439 -42.40985  38.87912

$BIC
[1] -6.420878

$pair.BIC
[1] -10.85297 -38.42844  42.86053

$AIC
[1] -1230.874

$pair.AIC
 [1]   51.064455   49.564629 -275.064075 -275.661120 -260.698047   -9.477981
 [7]  117.258206   88.256120  109.304104  133.670869  143.605391  134.791573
[13] -560.747289 -470.809333 -205.931355

$BIC
[1] -1111.431

$pair.BIC
 [1]   59.027283   57.527458 -267.101246 -267.698291 -252.735219   -1.515153
 [7]  125.221035   96.218948  117.266932  141.633697  151.568219  142.754402
[13] -552.784461 -462.846504 -197.968527

$AIC
[1] 179.9519

$pair.AIC
[1]   -7.094134   -3.092514 -100.740776  -26.419653  -12.400389  329.699337

$BIC
[1] 207.8218

$pair.BIC
[1]  -3.1127195   0.8889002 -96.7593621 -22.4382391  -8.4189752 337.6621655