High Performance Algorithms for Vine Copula Modeling • rvinecopulib
Description: Provides an interface to vinecopulib, a C++ library for vine copula modeling. The rvinecopulib package implements the core features of the popular VineCopula package, in particular inference algorithms for both vine copula and bivariate copula models. Advantages over VineCopula are a sleeker and more modern API, improved performances, especially in high dimensions, nonparametric and multi-parameter families, and the ability to model discrete variables. The rvinecopulib package includes vinecopulib as header-only C++ library (currently version 0.6.2). Thus users do not need to install vinecopulib itself in order to use rvinecopulib. Since their initial releases, vinecopulib is licensed under the MIT License, and rvinecopulib is licensed under the GNU GPL version 3.

# rvinecopulib

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, * ability to model discrete variables.

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.

## Table of contents

- rvinecopulib
  - Table of contents
  - How to install
  - Package overview
    - Bivariate copula modeling: bicop_dist and bicop
    - Vine copula modeling: vinecop_dist and vinecop
    - Bivariate copula families
  - References

## How to install

You can install:

- the stable release on CRAN:

      install.packages("rvinecopulib")

- the latest development version:

      remotes::install_github("vinecopulib/rvinecopulib")

## 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: bicop_dist and bicop

- `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.

### Vine copula modeling: vinecop_dist and vinecop

- `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.

### 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. Additionally, nonparametric families are also supported.

type | name | name in R
--- | --- | ---
- | Independence | “indep”
Elliptical | Gaussian | “gaussian”
” | Student t | “t”
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 (`"t"`, `"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]`

## 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.