CDVineSeqEst: Sequential estimation 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

This function sequentially estimates the pair-copula parameters of d-dimensional C- or D-vine copula models.

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CDVineSeqEst(data, family, type, method="mle", se=FALSE, max.df=30,
             max.BB=list(BB1=c(5,6),BB6=c(6,6),BB7=c(5,6),BB8=c(6,1)),
             progress=FALSE)

`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)
`type`	Type of the vine model: `1` or `"CVine"` = C-vine `2` or `"DVine"` = D-vine
`method`	Character indicating the estimation method: either pairwise maximum likelihood estimation (`method = "mle"`; default) or inversion of Kendall's tau (`method = "itau"`; see `BiCopEst`). For `method = "itau"` only one parameter pair-copula families can be used (`family = 1`, `3`, `4`, `5`, `6`, `13`, `14`, `16`, `23`, `24`, `26`, `33`, `34` or `36`).
`se`	Logical; whether standard errors are estimated (default: `se=FALSE`).
`max.df`	Numeric; upper bound for the estimation of the degrees of freedom parameter of the t-copula (default: `max.df = 30`; for more details see `BiCopEst`).
`max.BB`	List; upper bounds for the estimation of the two parameters (in absolute values) of the BB1, BB6, BB7 and BB8 copulas (default: `max.BB = list(BB1=c(5,6),BB6=c(6,6),BB7=c(5,6),BB8=c(6,1))`).
`progress`	Logical; whether the pairwise estimation progress is printed (default: `progress = FALSE`).

The pair-copula parameter estimation is performed tree-wise, i.e., for each C-/D-vine tree the results from the previous tree(s) are used to calculate the new copula parameters using BiCopEst.

`par`	Estimated (first) C-/D-vine pair-copula parameters.
`par2`	Estimated second C-/D-vine pair-copula parameters for families with two parameters (t, BB1, BB6, BB7, BB8). All other entries are zero.
`se`	Estimated standard errors of the (first) pair-copula parameter estimates (if `se = TRUE`).
`se2`	Estimated standard errors of the second pair-copula parameter estimates (if `se = TRUE`).

Carlos Almeida, Ulf Schepsmeier

Aas, K., C. Czado, A. Frigessi, and H. Bakken (2009). Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics 44 (2), 182-198.

Czado, C., U. Schepsmeier, and A. Min (2012). Maximum likelihood estimation of mixed C-vines with application to exchange rates. Statistical Modelling, 12(3), 229-255.

BiCopEst, BiCopHfunc, CDVineLogLik, CDVineMLE

## Example 1: 4-dimensional D-vine model with Gaussian pair-copulas
data(worldindices)
Data = as.matrix(worldindices)[,1:4]
d = dim(Data)[2]
fam = rep(1,d*(d-1)/2)

# sequential estimation 
CDVineSeqEst(Data,fam,type=2,method="itau")$par
CDVineSeqEst(Data,fam,type=2,method="mle")$par


## Example 2: 4-dimensional D-vine model with mixed pair-copulas
fam2 = c(5,1,3,14,3,2)

# sequential estimation
CDVineSeqEst(Data,fam2,type=2,method="mle",se=TRUE,progress=TRUE)

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.

[1] 0.1599446 0.3122243 0.1901583 0.1153481 0.1945338 0.6941092
[1] 0.2017503 0.3246330 0.1901583 0.1190999 0.2154168 0.7265423
1,2
2,3
3,4
1,3|2
2,4|3
1,4|2,3
$par
[1] 0.9154534 0.3246330 0.1916378 1.0688747 0.2340853 0.7185443

$par2
[1] 0.000000 0.000000 0.000000 0.000000 0.000000 7.802587

$se
[1] 0.30291987 0.04249825 0.06049709 0.02975006 0.06241570 0.02439815

$se2
[1] 0.000000 0.000000 0.000000 0.000000 0.000000 4.374521