Provides tools for the statistical analysis of regular vine copula
models, see Aas et al. (2009)
Vine copulas are a flexible class of dependence models consisting of bivariate building blocks (see e.g., Aas et al., 2009). You can find a comprehensive list of publications and other materials on vine-copula.org.
This package is primarily made for the statistical analysis of vine copula models. The package includes tools for parameter estimation, model selection, simulation, goodness-of-fit tests, and visualization. Tools for estimation, selection and exploratory data analysis of bivariate copula models are also provided. Please see the API documentation for a detailed description of all functions.
You can install:
the stable release on CRAN:
install.packages("VineCopula")
the latest development version:
devtools::install_github("tnagler/VineCopula")
Below, we list most functions and features you should know about. As usual in copula models, data are assumed to be serially independent and lie in the unit hypercube.
BiCop
: Creates a bivariate copula by specifying the family and parameters
(or Kendall's tau). Returns an object of class BiCop
. The class has the
following methods:
print
, summary
: a brief or comprehensive overview of the bivariate
copula, respectively.
plot
, contour
: surface/perspective and contour plots of the copula
density. Possibly coupled with standard normal margins (default for
contour
).
BiCopSim
: Simulates from a bivariate copula.
BiCopEst
: Estimates parameters of a bivariate copula with a prespecified
family. Estimation can be done by maximum likelihood (method = "mle"
) or
inversion of the empirical Kendall's tau (method = "itau"
, only available
for one-parameter families). Returns an object of class BiCop
.
BiCopSelect
: Estimates the parameters of a bivariate copula for a set
of families and selects the best fitting model (using either AIC or BIC).
Returns an object of class BiCop
.
BiCopGofTest
: Goodness-of-Fit tests for bivariate copulas.
BiCopVuongClarke
: Vuong and Clarke tests for model comparison within a
prespecified set of copula families.
BiCopPar2Tau
, BiCopTau2Par
, BiCopPar2Beta
, BiCopPar2TailDep
:
Conversion between dependence measures and parameters (for a given family).
Functions are vectorized in all arguments.
Evaluate functions related to a bivariate copula: BiCopPDF
, BiCopCDF
,
BiCopDeriv
, BiCopDeriv2
, BiCopHfunc
, BiCopHfuncDeriv
,
BiCopHfuncDeriv2
, BiCopHinv
. Functions are vectorized in the family
,
par
, and par2
arguments.
BiCopKDE
: Kernel density plots for copula data.
BiCopLambda
, BiCopKPlot
, BiCopChiPlot
: Further plot types for the
analysis of bivariate copulas.
For most functions, you can provide an object of class BiCop
instead of
specifying family
, par
and par2
manually.
RVineMatrix
: Creates a vine copula model by specifying structure, family
and parameter matrices. Such matrices have been introduced by Dissman et al.
(2013). Returns an object of class RVineMatrix
. The class has
the following methods:
plot
: Plots the trees of the the R-vine tree structure. Optionally,
you can annotate the edges with pair-copula families and parameters.
contour
: Creates a matrix of contour plots associated with the
pair-copulas.
RVineSim
: Simulates from a vine copula model.
RVineSeqEst
: Estimates the parameters of a vine copula model with
prespecified structure and families.
RVineCopSelect
: Estimates the parameters and selects the best family for a
vine copula model with prespecified structure matrix.
RVineStructureSelect
: Fits a vine copula model assuming no prior knowledge.
It selects the R-vine structure using Dissmann et al. (2013)'s
method, estimates parameters for various families, and selects the best
family for each pair.
RVineGoFTest
: Goodness-of-Fit tests for a vine copula model (c.f.,
Schepsmeier, 2013, 2015). Related functions are RVineGrad
,
RVineHessian
, RVineStdError
, and RVinePIT
.
RVineVoungTest
, RVineClarkeTest
: Vuong and Clarke tests for comparing
two vine copula models.
RVinePar2Tau
, RVinePar2Beta
: Calculate dependence measures
corresponding to a vine copula model.
RVinePDF
, RVineLogLik
, RVineAIC
, RVineBIC
: Calculate the density,
log-likelihood, AIC, and BIC of a vine copula.
The functions C2RVine
and D2RVine
create RVineMatrix
objects for C- and
D-vine copulas. This is particularly useful for former users of the CDVine
package.
Furthermore, bivariate and vine copula models from this packages can be used
with the copula package
(Hofert et al., 2015). For example, vineCopula
transforms an RVineMatrix
object into an object of class vineCopula
which provides methods for
dCopula
, pCopula
, and rCopula
. For more details, we refer to the package
manual.
In this package several bivariate copula families are included for bivariate and multivariate analysis using vine copulas. It provides functionality of elliptical (Gaussian and Student-t) as well as Archimedean (Clayton, Gumbel, Frank, Joe, BB1, BB6, BB7 and BB8) copulas to cover a large range of dependence patterns. For Archimedean copula families, rotated versions are included to cover negative dependence as well.
The Tawn copula is an asymmetric extension of the Gumbel copula with three parameters. For simplicity, we implemented two versions of the Tawn copula with two parameters each. Each type has one of the asymmetry parameters fixed to 1, so that the corresponding copula density is either left- or right-skewed (in relation to the main diagonal). In the manual we will call these two new copulas "Tawn type 1" and "Tawn type 2".
The following table shows the parameter ranges of bivariate copula families with
parameters par
and par2
and internal coding family
:
Copula family | family |
par |
par2 |
---|---|---|---|
Gaussian | 1 |
(-1, 1) |
- |
Student t | 2 |
(-1, 1) |
(2,Inf) |
(Survival) Clayton | 3 , 13 |
(0, Inf) |
- |
Rotated Clayton (90 and 270 degrees) | 23 , 33 |
(-Inf, 0) |
- |
(Survival) Gumbel | 4 , 14 |
[1, Inf) |
- |
Rotated Gumbel (90 and 270 degrees) | 24 , 34 |
(-Inf, -1] |
- |
Frank | 5 |
R \ {0} |
- |
(Survival) Joe | 6 , 16 |
(1, Inf) |
- |
Rotated Joe (90 and 270 degrees) | 26 , 36 |
(-Inf, -1) |
- |
(Survival) Clayton-Gumbel (BB1) | 7 , 17 |
(0, Inf) |
[1, Inf) |
Rotated Clayton-Gumbel (90 and 270 degrees) | 27 , 37 |
(-Inf, 0) |
(-Inf, -1] |
(Survival) Joe-Gumbel (BB6) | 8 , 18 |
[1 ,Inf) |
[1, Inf) |
Rotated Joe-Gumbel (90 and 270 degrees) | 28 , 38 |
(-Inf, -1] |
(-Inf, -1] |
(Survival) Joe-Clayton (BB7) | 9 , 19 |
[1, Inf) |
(0, Inf) |
Rotated Joe-Clayton (90 and 270 degrees) | 29 , 39 |
(-Inf, -1] |
(-Inf, 0) |
(Survival) Joe-Frank (BB8) | 10 , 20 |
[1, Inf) |
(0, 1] |
Rotated Joe-Frank (90 and 270 degrees) | 30 , 40 |
(-Inf, -1] |
[-1, 0) |
(Survival) Tawn type 1 | 104 , 114 |
[1, Inf) |
[0, 1] |
Rotated Tawn type 1(90 and 270 degrees) | 124 , 134 |
(-Inf, -1] |
[0, 1] |
(Survival) Tawn type 2 | 204 , 214 |
[1, Inf) |
[0, 1] |
Rotated Tawn type 2 (90 and 270 degrees) | 224 , 234 |
(-Inf, -1] |
[0, 1] |
This small shiny app enables the user to draw nice tree plots of an R-Vine
copula model using the package
d3Network. Models have to be
set up locally in an RVineMatrix
object and uploaded as .RData file. The page
is still under construction.
Author: Ulf Schepsmeier
https://rvinegraph.shinyapps.io/rvinegraph
Aas, K., C. Czado, A. Frigessi, and H. Bakken (2009). Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics 44 (2), 182-198.
Bedford, T. and R. M. Cooke (2001). Probability density decomposition for conditionally dependent random variables modeled by vines. Annals of Mathematics and Artificial intelligence 32, 245-268.
Bedford, T. and R. M. Cooke (2002). Vines - a new graphical model for dependent random variables. Annals of Statistics 30, 1031-1068.
Brechmann, E. C., C. Czado, and K. Aas (2012). Truncated regular vines in high dimensions with applications to financial data. Canadian Journal of Statistics 40 (1), 68-85.
Brechmann, E. C. and C. Czado (2011). Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50. Statistics & Risk Modeling, 30 (4), 307-342.
Brechmann, E. C. and U. Schepsmeier (2013). Modeling Dependence with C- and D-Vine Copulas: The R Package CDVine. Journal of Statistical Software, 52 (3), 1-27. http://www.jstatsoft.org/v52/i03/.
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.
Dissmann, J. F., E. C. Brechmann, C. Czado, and D. Kurowicka (2013). Selecting and estimating regular vine copulae and application to financial returns. Computational Statistics & Data Analysis, 59 (1), 52-69.
Eschenburg, P. (2013). Properties of extreme-value copulas Diploma thesis, Technische Universitaet Muenchen http://mediatum.ub.tum.de/node?id=1145695.
Hofert, M., I. Kojadinovic, M. Maechler, and J. Yan (2015). copula: Multivariate Dependence with Copulas. R package version 0.999-13 https://cran.r-project.org/package=VineCopula
Joe, H. (1996). Families of m-variate distributions with given margins and m(m-1)/2 bivariate dependence parameters. In L. Rueschendorf, B. Schweizer, and M. D. Taylor (Eds.), Distributions with fixed marginals and related topics, pp. 120-141. Hayward: Institute of Mathematical Statistics.
Joe, H. (1997). Multivariate Models and Dependence Concepts. London: Chapman and Hall.
Knight, W. R. (1966). A computer method for calculating Kendall's tau with ungrouped data. Journal of the American Statistical Association 61 (314), 436-439.
Kurowicka, D. and R. M. Cooke (2006). Uncertainty Analysis with High Dimensional Dependence Modelling. Chichester: John Wiley.
Kurowicka, D. and H. Joe (Eds.) (2011). Dependence Modeling: Vine Copula Handbook. Singapore: World Scientific Publishing Co.
Nelsen, R. (2006). An introduction to copulas. Springer
Nagler, T. (2015). kdecopula: Kernel Smoothing for Bivariate Copula Densities. R package version 0.6.0. https://cran.r-project.org/package=kdecopula
Schepsmeier, U. and J. Stoeber (2012). Derivatives and Fisher information of bivariate copulas. Statistical Papers, 55 (2), 525-542. http://link.springer.com/article/10.1007/s00362-013-0498-x.
Schepsmeier, U. (2013) A goodness-of-fit test for regular vine copula models. Preprint. http://arxiv.org/abs/1306.0818.
Schepsmeier, U. (2015) Efficient information based goodness-of-fit tests for vine copula models with fixed margins. Journal of Multivariate Analysis 138, 34-52.
Stoeber, J. and U. Schepsmeier (2013). Estimating standard errors in regular vine copula models. Computational Statistics, 28 (6), 2679-2707 http://link.springer.com/article/10.1007/s00180-013-0423-8.
White, H. (1982) Maximum likelihood estimation of misspecified models, Econometrica, 50, 1-26.
BUG FIXES
BiCopHfuncDeriv(2)
(non-critical).BUG FIXES
get rid of warning messages when checking whether structure is a D-vine.
fix standard errors for one-parameter families.
avoid infinite loop for Joe's inverse h-function with extreme parameter values.
fix parameters bounds for BB copulas in RVineMLE()
.
BUG FIXES
fix rotation handling in derivative calculations.
fix check for whether a structure is a D-vine.
fixed typos in API documentation.
NEW FEATURES
BUG FIXES
fix calculation of Kendall's tau when joint ties are present.
fix missing pair.AIC/BIC
in RVineSeqEst()
.
improved starting parameter for Joe copula MLE.
NEW FEATURES
All C-headers are now located in inst/include/VineCopula
(#48).
Most C routines are registered as C-callable (#47).
BUG FIXES
RVineMLE
can now safely called with only independence copulas (#49).
Fixed fix (non-critical) memory-access bug.
NEW FEATURES
summary.RVineMatrix()
invisibly returns a data.frame
containg most of
what is printed as output.
Less restrictive conditions on what is considered an appropriate treecrit
function in RVineStructureSelect()
(thanks to Thibault Vatter, #40).
New option verbose
in RVinePDF()
(thanks to @cag51, #36).
BUG FIXES
Fix parameter bounds in RVineMLE()
corresponding to updated requirements
in BiCop
-functions.
Adapt to re-naming of tailIndex
to lambda
in the copula package (thanks
to Benedikt Graeler, #41, #42).
Fix bug in detecting C-vine copulas for summary/print.RVineMatrix()
(#38).
NEW FEATURES
Online API documentation on https://tnagler.github.io/VineCopula/.
Faster BiCopCDF()
.
BUG FIXES
Fixed bug in preprocessing of weights
argument.
More informative error message when family is unknown.
Safer BiCopSelect()
with presel = TRUE
and insufficient data.
Fixed RVineMatrix()
(output dimension was d-1
and naturalOrder = TRUE
wasn't working, thanks @tvatter).
Safer BiCopEst()
for method = "itau"
.
IMPORTS
copula (>= 0.999-16)
. The new version of copula
requires VineCopula to be re-installed, because the old fitCopula()
method doesn't work any longer, but was re-exported by VineCopula.NEW FEATURES
LinkingTo
field.R (>= 3.1.0)
. So far, this dependence was
implicit trhough our dependence on the copula package.NEW FEATURES
All estimation functions now have a method
argument. The default is
method = "mle"
and corresponds to the old behavior. The other option,
method = "itau"
, estimates the parameters by inversion of Kendall's. It is
much faster than method = "mle"
, but is only available for one-parameter
families and the t-copula. Big thanks to Thibault Vatter who did most of the
work (PR #25).
New function RVineMatrixSample
that randomly generates valid R-vine
matrices using the algorithm of Joe et al. (2011). Contributed by
Thibault Vatter (PR #27).
Faster versions of RVineMatrix
and RVineCopSelect
, and
RVineStructureSelect
by avoiding unnecessary computations (thanks to
Thibault Vatter, PRs #29 and #31).
All -Select
functions now have a presel
argument. If TRUE
(default)
the familyset is reduced to families that have asymmetry charactistics that
conform with the observed data.
RVineSim
, RVineLogLik
, and RVinePDF
have been implemented in a way
that demands less memory. For RVineLogLik
, the option calculate.V
has
to be set to TRUE
.
BUG FIXES
Fixed bug in upper tail dependence coefficient for survival BB1 (reported by Viviana Fernandez, thanks!).
RVineStructureSelect
now works in dimension two as well.
RVineMatrixCheck
returns the new error code -4
when the matrix is
neither lower nor upper triangular (threw an actual error before).
contour.RVineMatrix
now arranges the contour matrix conforming with the
family and parameter matrices.
DEPENDS
BUG FIXES
Use se = FALSE
as default throughout the package for faster estimation.
Fixed errors in BiCopGofTest
for the Student t copula and par2
close to
2 and for most other families for tau
close to 0 (reported by Thong Huy
Nguyen, thanks!).
Fix sign in starting parameters for Tawn MLE.
Fixed storage positions of par2
in output matrix of RVineMLE
(reported
by Robin Evans, thanks!).
NEW FEATURES
contour.RVineMAtrix
.BUG FIXES
Return scalar instead of 1-dim array in tau <-> par conversion.
Fix vectorized call of BiCopCDF
.
Negative selection of families is now working properly.
Correct logLik calculation in output of RVineMLE
.
Dependence measures are updated in output of RVineCor2pcor
.
Fix bug in annotation of edges with Kendall's when using plot.RVineMatrix
.
BUG FIXES
MAINTAINER
DEPENDS
igraph has been removed from Imports
.
network has been added to Imports
.
NEW FEATURES
All functions in the package can now handle NAs in the data. A warning message indicates presence of NAs and explains how they are treated.
Extend BiCop
and RVineMatrix
objects (now include: associated dependence
measures; fit statistics and p-values, if available).
New methods print
and summary
for objects of class BiCop
and
RVineMatrix
.
New plotting generics:
plot.RVineMatrix
for plotting vine trees,
contour.RVineMatrix
for a matrix of contour plots,
contour.BiCop
as short hand for plot.BiCop(..., type = "contour")
.
Vectorize BiCopXyz
-functions w.r.t. family
, par
, par2
:
in C: BiCopPDF
, BiCopHfunc
, BiCopHinv
, BiCopDeriv
, BiCopDeriv2
,
BiCopHfuncDeriv
, BiCopHfuncDeriv2
.
in R: BiCopCDF
, BiCopPar2Tau
, BiCopPar2Beta
, BiCopPar2TailDep
.
Etimation of vine copulas
(RVineStructureSelect
, RVineCopSelect
, RVineSeqEst
) can now be done in
parallel using the cores
argument (based on foreach
) and is more memory
efficient (pseudo-observations are discarded as soon they are useless).
RVineStructureSelect
now takes an argument treecrit
allowing for
several preimplemented (and custom) choices of the edge weight used in
Dissmann's algorithm.
Treatment of familyset
in the -Select functions:
independence copula is handled as a regular family,
negative integers can be used to select from all but a subset of families.
New function BiCopCompare
: A shiny app where the user can visually assess
how well several families fit the data.
New function BiCopKDE
for kernel density plots (based on kdecopula
package).
New function BiCopCondSim
for conditional simulation from a bivariate
copula.
New function BiCopHinv
for computation of inverse h-functions.
New functions BiCopHfunc1
, BiCopHfunc2
, BiCopHinv1
, and BiCopHinv2
that only compute one of the two h-functions (or inverse h-functions).
New function BiCopCheck
for checking of family/parameter
consistency.
Add check.pars
/check.taus
argument to the above functions for the option
to omit family/parameter consistency checks (for internal usage). When
FALSE
, the Clayton and Frank copulas can be used with par = 0
.
Faster implementations of BiCopPar2Tau
/BiCopTau2Par
for Frank copula and
BiCopTau2Par
conversion for Joe copula.
BUG FIXES
Correct call for non-t families in BiCopHfuncDeriv2(..., deriv = "par1u2")
.
The S4-class objets of the Tawn copulas pointed to Archimedean CDFs, now corrected to true CDFs based on C-code.
TauMatrix
: restriction for input data to be in [0,1] removed.
RVineCopSelect
: no printing of family matrix.
Added methods for Pickand's dependence function "A" for tawnT1Copula
,
surTawnT1Copula
, tawnT2Copula
and surTawnT2Copula
.
Use C-code instead of R-code and remove redundant C-code of Tawn copulas.
Small bug fix in log-likelihood for families 3, 4, 7, 17.
Increased upper limit for uniroot in Joe.itau.JJ
.
Fixed rotations of Tawns (they were actually reflection w.r.t. the axes u = 0.5 and u2 = 0.5)
Correct calculation of the goodness-of-fit test based on Whites Information
matrix test for bivariate copulas BiCopGofTest(..., method = "white")
.
The variance matrix needed for the test statistic had a poor approximation.
Thereby the asymptotic p-values are corrected.
Bound parameter ranges for Archimedean copulas to avoid numerical instabilities in -PDF and -Sim functions.
DEPENDS:
BUG FIXES:
NEW FEATURES
RVineTreePlot
: option for a legend (and numbered nodes and edges).BUG FIXES
Definition of "C" in BiCopCDF for tawn copulas used constants u1
and u2
instead of arguments u
and v
.
RVineStructureSelect
: Adjust to new version of igraph. Tree structure was
not selected correctly. igraph function names changed to the names used in
the new version. Some small modifications to avoid some for loops and make
the code easier to read.
IMPORTS
Extend Imports to avoid undefined globals (CRAN E-mail 02.07.2015).
New version requires igraph (>= 1.0.0)
.
NEW FEATURES
as.copuladata
: coerce to class copuladata
.
pairs.copuladata
: pairs
plots for objects of class copuladata
.
RVinePDF
: PDF of an R-Vine Copula Model.
BiCopSelect
, RVineCopSelect
, RVineStructureSelect
: add option
rotations = TRUE
which augments the familyset with all rotations to a
given family.
RVineMatrix
, RVineStructureSelect
: allow upper triangular matrices as
input (output remains lower triangular).
BiCop
objects for bivariate copulas:
add constructor BiCop
and plotting generic plot.BiCop
.
define results of BiCopEst
/BiCopSelect
as BiCop
objects.
add compatibility with other BiCopXyz
functions (BiCopPDF
,
BiCopPar2Tau
, etc.).
BUG FIXES
BiCopEst
: extend search interval for Tawn MLE to avoid optim
-errors.
BiCopEst
: fix for optim error ('non-finite value supplied').
RVineSim
: reorder U
so that it corresponds to the order of RVM
.
RVineCor2pcor
: include normalization step for a more intuitive behavior,
bug fix for $d = 2, 3$ and $d > 9$.
RVinePcor2cor
: bug fixes for $d = 2$ and $d > 9$.
RVineCopSelect
: RVM
object now uses variable names as provided by data.
NEW FEATURES
BiCopTau2Par
and BiCopPar2Tau
: fully vectorized (parameter/tau input),
and sanity checks extended. Before vector input was not prohibited.
However, both functions were not intended to be used for vectorized input.NEW AUTHOR
NEW FEATURES
BUG FIXES
RVineStructureSelect
: Bug concerning the dimensions of input data/security
queries fixed (Reported by Sarka Cerna, Radek Solnicky and Ludovic Theate.
Thanks a lot!)
RVineStructureSelect
: Correct handling of rotated BBs and Tawns.
BiCopSelect
, BiCopEst
: Improved starting values for Tawn MLE.
hfunc.c
:
Correct Hfunc1
for Tawns.
Bound all results to lie in 0,1
Extension of Hinv1
and Hinv2
in analogy to Hfunc1
and Hfunc2
.
incompleteBeta.c
: Misuse of the C function abs (as reported by CRAN)
corrected to fabs
.
gof_PIT.R
: Use of require()
replaced by requireNamespace
according to
'Writing R Extensions'.
Package ADGofTest
removed from Suggests
(see 'Writing R Extensions'
for usage of Suggests).
Import of function ad.test
from ADGofTest
for gof_PIT.R
.
BUG FIXES
Bootstrap procedure for the White test (RVineGofTest
, gof_White
) was
incorrect.
(Reported by Piotr Zuraniewski and Daniel Worm. Thanks!)
Bootstrap procedure for the PIT based and the ECP based test were incorrect. First, C starts to count at 0 not 1. This could result in zero entries in the bootstrapped data matrix. Second, forget to permute vdirect and vindirect according to the permutation of data.
BiCopSelect
: For the rotated BB7 and BB8 (family = 37, 38
) the limiting
cases were incorrect for very small parameters (copy&paste error).
(Reported by Radek Solnicky. Thanks!)
MAINTAINER
NEW FEATURES
IMPORTS
Depends
to the more appropriate Import
field.NEW FEATURES
RVineSim
allows to commit a (N x d)
-matrix of $U[0,1]$ random variates
to be transformed to the copula sample. For example if you want to use quasi
random variables instead of the pseudo random variables implemented in R.
(Thanks to Marius Hofert)
The package now contains class wrappers that are compatible with the copula
class from the copula
R-package. These include all bivariate families
currently implemented: The class representation for different rotated
families of e.g the BB6 family are represented as BB6Copula
, r90B6Copula
,
surBB6Copula
and r270BB6Copula
. These bivariate classes are fully
compatible with the standard copula methods such as dCopula
, pCopula
,
rCopula
or fitCopula
including persp
and contour
. A vine copula can
as well be coerced into a class representation of vineCopula
. However,
the support of the standard methods is limited. See the corresponding help
pages for details. Earlier introduced R-wrapper of C-functions have been
removed, as they are no longer needed by the spcopula
R-package.
Added parameter verbose
to RVineLogLik
to allow to suppress some debug
output.
BUG FIXES
RVineMLE
: the optim
argument parscale
was not correctly defined for
all cases.
RVineAIC
/RVineBIC
: Instead of the function arguments par
and par2
the calculation was based on RVM$par
and RVM$par2
. This is corrected now.
(reported by Marcel Duellmann; thanks)
RVineStructureSelect
: The new igraph version returned a different
variable type causing an error in the second and higher order tree selection.
NEW FEATURES
RVinePIT
: calculation of the probability integral transform (PIT) for
R-vines.
RVineGofTest
: 15 different goodness-of-fit tests for R-vine copulas
(Schepsmeier 2013).
print.RVM
: A more detailed summary is printed if print(RVM, detail = TRUE)
is set.
BetaMatrix
: Matrix of empirical Blomqvist's beta values.
BiCopPar2Beta
: Blomqvist's beta value of a bivariate copula.
RVinePar2Beta
: Blomqvist's beta values of an R-vine copula model.
RVineCor2pcor
: correlations to partial correlations for R-vines.
RVinePcor2cor
: partial correlations to correlations for R-vines.
New copula families for most of the BiCop as well as for the
RVine
-functions:
As an asymmetric extension of the Gumbel copula, the Tawn copula with three parameters is now also included in the package. Both the Gumbel and the Tawn copula are extreme-value copulas, which can be defined in terms of their corresponding Pickands dependence functions.
For simplicity, we implemented two versions of the Tawn copula with two parameters each. Each type has one of the asymmetry parameters fixed to 1, so that the corresponding Pickands dependence is either left- or right-skewed. In the manual we will call these two new copulas "Tawn type 1" and "Tawn type 2".
The families 104
, 114
, 124
, 134
denote the Tawn copula and their
rotated versions in the case of left skewness (Tawn type 1).
The families 204
, 214
, 224
, 234
denote the Tawn copula and their
rotated versions in the case of right skewness (Tawn type 2).
BUG FIXES
BiCopPar2Tau
: corrected calculation of Kendall's tau of rotated BB7.
(Reported by Giampiero Marra. Thanks!)
RVineStructureSelect
: Corrected code for the igraph package.
RVineTreePlot
: Now a 3-dimensional R-vine can be plotted too.
Corrected upper tail dependence coefficient for the survival BB1 copula
(BiCopPar2TailDep
).
Minor improvement in BiCopSelect
regarding the starting values for
parameter estimation.
DOCUMENTAION
NEW AUTHOR
NEW FEATURES
Changed dependency from igraph0 to igraph since the support for igraph0 will be quit soon.
Additional validity check of the R-vine matrix in RVineMatrix
(Code
provided by Harry Joe). Also available as separate function
RVineMatrixCheck
.
New bivariate copula: Reflection asymmetric Archimedean copula. In our
functions it is family = 41, 51, 61, 71
( with rotated versions).
So far only implemented in some bivariate functions (not documented so
far; experimental).
BUG FIXES
New (correct) examples for the Clarke and Vuong test.
Fixed memory problem in the C-function ktau
(TauMatrix
).
BUG FIXES
NEW FEATURES
BiCopGofTest
: Goodness-of-fit test for bivariate copulas based on White's
information matrix equality as introduced by Wanling and Prokhorov (2011).
The formally included function BiCopGofKendall
is now part of
BiCopGofTest
(method = "kendall"
).
Additional edge label pair
in RVineTreePlot
to display the indices of
the (conditioned) pairs of variables identified by the edges.
In RVineStructureSelect
and RVineCopSelect
a truncation level can be set.
Improved inverse h-functions for the Gumbel and Joe copulas (thanks to Harry Joe).
C to R wrapping functions for the h-functions (Hfunc1
, Hfunc2
), the
bivariate log-likelihood function (LL_mod_seperate
), the bivariate
Archimedean copula CDF (archCDF
) and the simulation function for C- and
D-vines (pcc
) (request of Benedikt Graeler for the R-package spcopula
).
The functions R2CVine and R2Dine were removed, since they were only correct in special cases.
BUG FIXES
Work around for a problem with optim
and the analytical gradient in
BiCopEst
.
Improvement of the bivariate maximum likelihood estimation (BiCopEst
).
In the functions BiCopCDF
and BiCopGoFTest(..., method = "Kendall")
the
t-copula is not implemented any more. The calculation of the CDF was
incorrect for non-integer values of the degrees-of-freedom parameter. The
implemented algorithm in the mvtnorm
package only works for integer values
of the degrees-of-freedom parameter.
Improvement in the calculation of the cdf of the Frank copula (BiCopCDF
).