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 the R API to the C++ library vinecopulib, a header-only C++ library for vine copula models based on Boost and Eigen.

It provides high-performance implementations of the core features of the popular VineCopula R library, in particular inference algorithms for both vine copula and bivariate copula models. Advantages over VineCopula are

* a sleaker and more modern API, * shorter runtimes, especially in high dimensions, * nonparametric and multi-parameter families.

As VineCopula, the package is primarily made for the statistical analysis of **vine copula models**. The package includes tools for parameter estimation, model selection, simulation, 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:

the latest development version:

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_dist`

: Creates a bivariate copula by specifying the family, rotation and parameters. Returns an object of class`bicop_dist`

. The class has the following methods:`print`

: a brief overview of the bivariate copula.`plot`

,`contour`

: surface/perspective and contour plots of the copula density. Possibly coupled with standard normal margins (default for`contour`

).

`dbicop`

,`pbicop`

,`rbicop`

,`hbicop`

: Density, distribution function, random generation and H-functions (with their inverses) for bivariate copula distributions. Additionally to the evaluation points, you can provide either`family`

,`rotation`

and`parameter`

, or an object of class`bicop_dist`

.`bicop`

: Estimates parameters of a bivariate copula. Estimation can be done by maximum likelihood (`par_method = "mle"`

) or inversion of the empirical Kendall’s tau (`par_method = "itau"`

, only available for one-parameter families) for parametric families, and using local-likelihood approximations of order zero/one/two for nonparametric models (`nonpar_method="constant"`

/`nonpar_method="linear"`

/`nonpar_method="quadratic"`

). If`family_set`

is a vector of families, then the family is selected using`selcrit="loglik"`

,`selcrit="aic"`

or`selcrit="bic"`

. The function returns an object of classes`bicop`

and`bicop_dist`

. The class`bicop`

has the following following methods:`print`

: a more comprehensive overview of the bivariate copula model with fit statistics.`predict`

,`fitted`

: predictions and fitted values for a bivariate copula model.`nobs`

,`logLik`

,`AIC`

,`BIC`

: usual fit statistics.

`vinecop_dist`

: Creates a vine copula by specifying a nested list of`bicop_dist`

objects and a quadratic structure matrix. Returns an object of class`vinecop_dist`

. The class has the following methods:`print`

,`summary`

: a brief and more comprehensive overview of the vine copula.`plot`

: plots of the vine structure.

`dvinecop`

,`pvinecop`

,`rvinecop`

: Density, distribution function, random generation for vine copula distributions.`vinecop`

: automated fitting for vine copula models. The function inherits the parameters of`bicop`

. Optionally, a quadratic`matrix`

can be used as input to pre-specify the vine structure.`tree_crit`

describes the criterion for tree selection, one of`"tau"`

,`"rho"`

,`"hoeffd"`

for Kendall’s tau, Spearman’s rho, and Hoeffding’s D, respectively. Additionally,`threshold`

allows to threshold the`tree_crit`

and`trunc_lvl`

to truncate the vine copula, with`threshold_sel`

and`trunc_lvl_sel`

to automatically select both parameters. The function returns an object of classes`vinecop`

and`vinecop_dist`

. The class has the`vinecop`

has the following following methods:`print`

,`summary`

: a brief and more comprehensive overview of the vine copula with additional fit statistics information.`predict`

,`fitted`

: predictions and fitted values for a vine copula model.`nobs`

,`logLik`

,`AIC`

,`BIC`

: usual fit statistics.

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. Additionally, nonparametric families are also supported.

type | name | name in R |
---|---|---|

- | Independence | “indep” |

Elliptical | Gaussian | “gaussian” |

" | Student t | “student” |

Archimedean | Clayton | “clayton” |

" | Gumbel | “gumbel” |

" | Frank | “frank” |

" | Joe | “joe” |

" | Clayton-Gumbel (BB1) | “bb1” |

" | Joe-Gumbel (BB6) | “bb6” |

" | Joe-Clayton (BB7) | “bb7” |

" | Joe-Frank (BB8) | “bb8” |

Nonparametric | Transformation kernel | “tll” |

Note that several convenience vectors of families are included: * `"all"`

contains all the families * `"parametric"`

contains the parametric families (all except `"tll"`

) * `"nonparametric"`

contains the nonparametric families (`"indep"`

and `"tll"`

) * `"one_par"`

contains the parametric families with a single parameter (`"gaussian"`

, `"clayton"`

, `"gumbel"`

, `"frank"`

, and `"joe"`

) * `"two_par"`

contains the parametric families with two parameters (`"student"`

, `"bb1"`

, `"bb6"`

, `"bb7"`

, and `"bb8"`

) * `"elliptical"`

contains the elliptical families * `"archimedean"`

contains the archimedean families * `"BB"`

contains the BB families * `"itau"`

families for which estimation by Kendall’s tau inversion is available (`"indep"`

,`"gaussian"`

, `"student"`

,`"clayton"`

, `"gumbel"`

, `"frank"`

, `"joe"`

)

The following table shows the parameter ranges of bivariate copula families with one or two parameters:

Copula family | `par[1]` |
`par[2]` |
---|---|---|

Gaussian | `(-1, 1)` |
- |

Student t | `(-1, 1)` |
`(2,Inf)` |

Clayton | `(0, Inf)` |
- |

Gumbel | `[1, Inf)` |
- |

Frank | `R \ {0}` |
- |

Joe | `(1, Inf)` |
- |

Clayton-Gumbel (BB1) | `(0, Inf)` |
`[1, Inf)` |

Joe-Gumbel (BB6) | `[1 ,Inf)` |
`[1, Inf)` |

Joe-Clayton (BB7) | `[1, Inf)` |
`(0, Inf)` |

Joe-Frank (BB8) | `[1, Inf)` |
`(0, 1]` |

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