VineCopula

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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.

Table of contents


How to install

You can install:


Package overview

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.

Bivariate copula modeling: the BiCop-family

For most functions, you can provide an object of class BiCop instead of specifying family, par and par2 manually.

Vine copula modeling: the RVine-family

Additional features

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.

Bivariate copula families

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 a non-exchangable 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 (relative 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]

Associated shiny apps

rvinegraph

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


References

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.