CDVineMLE: Maximum likelihood estimation of C- and D-vine copula models
In CDVine: Statistical Inference of C- And D-Vine Copulas

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

This function calculates the MLE of C- or D-vine copula model parameters using sequential estimates as initial values (if not provided).

1 2	CDVineMLE(data, family, start=NULL, start2=NULL, type, maxit=200, max.df=30, max.BB=list(BB1=c(5,6),BB6=c(6,6),BB7=c(5,6),BB8=c(6,1)), ...)

`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)
`start`	A d*(d-1)/2 numeric vector of starting values for C-/D-vine pair-copula parameters (optional; otherwise they are calculated via `CDVineSeqEst`; default: `start = NULL`).
`start2`	A d*(d-1)/2 numeric vector of starting values for second C-/D-vine pair-copula parameters (optional; otherwise they are calculated via `CDVineSeqEst`; default: `start2 = NULL`).
`type`	Type of the vine model: `1` or `"CVine"` = C-vine `2` or `"DVine"` = D-vine
`maxit`	The maximum number of iteration steps (optional; default: `maxit = 200`).
`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))`).
`...`	Additional control parameters for `optim`.

`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.
`loglik`	Optimized log-likelihood value corresponding to the estimated pair-copula parameters.
`convergence`	An integer code indicating either successful convergence (`convergence = 0`) or an error (cp. `optim`; the CDVineMLE-function uses the "L-BFGS-B" method): `1` = the iteration limit `maxit` has been reached `51` = a warning from the "L-BFGS-B" method; see component `message` for further details `52` = an error from the "L-BFGS-B" method; see component `message` for further details
`message`	A character string giving any additional information returned by `optim`, or `NULL`.

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.

CDVineLogLik, CDVineSeqEst

## Example 1: 4-dimensional D-vine model with Gaussian pair-copulas
data(worldindices)
Data = as.matrix(worldindices)[,1:4]
fam = rep(1,6)

# maximum likelihood estimation
## Not run: 
CDVineMLE(Data,family=fam,type=2,maxit=100)

## End(Not run)

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

# sequential estimation
m = CDVineSeqEst(Data,family=fam2,type=2)
m

# calculate the log-likelihood
LogLik0 = CDVineLogLik(Data,fam2,m$par,m$par2,type=2)
LogLik0$loglik

# maximum likelihood estimation
## Not run: 
CDVineMLE(Data,family=fam2,type=2,maxit=5)  # 5 iterations
CDVineMLE(Data,family=fam2,type=2)  # default: 200 iterations

## End(Not run)

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.

$par
[1] 0.2014844 0.3243304 0.1894926 0.1191447 0.2154987 0.7265817

$par2
[1] 0 0 0 0 0 0

$loglik
[1] 201.1419

$counts
function gradient 
       7        7 

$convergence
[1] 0

$message
[1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"

$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

[1] 198.2273
$par
[1] 0.8552650 0.3243652 0.1962937 1.0725591 0.1668017 0.7219322

$par2
[1] 0.000000 0.000000 0.000000 0.000000 0.000000 7.802131

$loglik
[1] 199.0857

$counts
function gradient 
       8        8 

$convergence
[1] 1

$message
[1] "NEW_X"

$par
[1] 0.6492769 0.3077149 0.1822637 1.0705138 0.1478432 0.7254859

$par2
[1] 0.00000 0.00000 0.00000 0.00000 0.00000 7.38417

$loglik
[1] 199.4444

$counts
function gradient 
      43       43 

$convergence
[1] 0

$message
[1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"